President Trump on Saturday accused Democrats of refusing to fund the United States Postal Service as he faced intense criticism from Democrats who say slowdowns in mail delivery, the removal of sorting machines and other changes are threatening the integrity of the general election.

Speaking at a news conference at his golf resort in Bedminster, N.J., Mr. Trump also continued to rail against mail-in voting, calling it “a catastrophe.” But he did not directly say whether he supported the removal of mail-sorting machines and other changes made under the leadership of his postmaster general, Louis DeJoy.

“I don’t know what he’s doing,” Mr. Trump said. “I can only tell you he’s a very smart man. He’ll be a great Postmaster General.”

Democrats have, in fact, pushed for a total of $10 billion for the Postal Service in talks with Republicans on the COVID-19 response bill. That figure, which would include money to help with election mail, was down from a $25 billion plan in a House-passed coronavirus measure.

Speaker Nancy Pelosi of California and House Democratic leadership have begun discussing bringing the chamber back early to address the issues with the Postal Service, a move that would cut short the annual summer recess. While the House is not scheduled to return for votes until Sept. 14, Democratic leaders could call lawmakers back in the next two weeks, two people familiar with the talks said on Saturday.

Among the legislative options under consideration include a measure put forward by Representative Carolyn B. Maloney of New York, the chairwoman of the House Oversight Committee, that would prohibit agency leadership from enacting any operational changes that were in place before Jan. 1 or once the public health crisis subsides. Such changes would include ending overtime pay or any measures that would delay mail. Lawmakers are also discussing adding language to the bill that would ensure all ballot-related mail is considered First Class Mail and treated as such.

While Democrats have been fighting to include funding for the Postal Service in a coronavirus relief package, it is unlikely that Democrats would act on a standalone funding bill, said the two people, who asked for anonymity in order to disclose details of private discussions, because the current crisis the agency is facing is tied to policy, not funding.

Mr. Trump on Saturday also refused to say that Kamala Harris, the Democratic vice-presidential running mate, is eligible for the vice presidency, but insisted he was not stoking a racist conspiracy theory that has taken hold among some of his followers.

“I have not gotten into it in great detail,” Mr. Trump said, when asked if Ms. Harris is eligible for the vice presidency. “If she’s got a problem, you would have thought that she would have been vetted. You would have thought that she would have been vetted by Sleepy Joe.”

In fact, Ms. Harris, the daughter of Jamaican and Indian immigrants, who was born in 1964 in Oakland, Calif., is eligible to serve as president or vice president. There is no basis for the conspiracy theory.

“I just don’t know about it, but it’s not something that we will be pursuing,” Mr. Trump said.

But he also praised John C. Eastman, a conservative lawyer who wrote a widely discredited op-ed article written in Newsweek that sought to raise questions about Ms. Harris’s eligibility. Mr. Trump called Mr. Eastman “a brilliant lawyer.”

Newsweek apologized on Saturday for publishing the op-ed, saying it was “being used by some as a tool to perpetuate racism and xenophobia.”

The Democratic National Convention kicks off Monday, and the uncertainties around it are legion.

Can a virtual political convention unfolding in the midst of a pandemic be compelling? How will the speakers inject energy into their performances when they have no audience cheering them on? Will the American people tune in, or is everyone sick of their screens?

Here are five questions to consider — around convention logistics and more traditional political issues alike — heading into a critical week for Democrats.

Can the Democrats unite their party — and win over any Republicans? Despite the extraordinary circumstances of this year’s event, more traditional convention imperatives — energizing the party and engaging swing voters — remain, too. Monday will offer a vivid illustration of the broad coalition the Democrats are hoping to assemble.

Michelle Obama, the former first lady, is the headliner, but the lineup also includes both Senator Bernie Sanders of Vermont, Joseph R. Biden Jr.’s progressive primary rival, and former Gov. John Kasich, Republican of Ohio.

As Mr. Biden seeks to excite skeptical liberals while reaching out to moderates disillusioned with President Trump, Monday will demonstrate how Democrats hope to thread that needle.

Will the technology cooperate? When Mr. Biden held a “virtual town hall” event in March, things did not go exactly as planned. Since then, America has settled in to communicating via video, but the technology risks at the convention are real. Will the satellite feeds hold? Will prominent participants accidentally mute — or unmute — themselves? Will anyone be interrupted while recording at home by well-meaning visitors, “BBC dad”-style?

The remote style of the convention, however, also brings opportunity. Speakers have been encouraged to seek out interesting locations for their backdrops. Who will claim the most iconic spot?

Can the candidates create any drama? Some politicians — Mr. Biden chief among them — thrive off audience reaction. How will he and other speakers build to crescendos and electrify viewers when there is no enthralled crowd cheering them on?

This past week, when Mr. Biden debuted with his running mate, Senator Kamala Harris, they had only the cameras and a group of journalists to wave to.

Will any new faces emerge? Conventions offer an unmatched platform for up-and-coming politicians to leave an impression in front of a national audience — just ask Barack Obama, whose keynote address at the 2004 convention was a pivotal moment in his rapid ascent from state senator to U.S. senator to president.

Even in a virtual format, there is still plenty of opportunity to get on people’s radar across the country. Who will make the most of that chance?

How will Trump respond? One thing is certain: The convention will place a lot of attention on a lot of Democratic politicians who are not fond of Mr. Trump. And Mr. Trump is unlikely to be restrained in his commentary next week.

One of the most powerful speeches of the 2016 Democratic convention came from Khizr Khan, the father of a Muslim American soldier who was killed while serving in Iraq. Mr. Khan denounced Mr. Trump’s campaign message, and Mr. Trump proceeded to attack Mr. Khan and his wife, igniting a political firestorm. Will a similar dynamic play out next week?

Protesters in Washington called for the resignation of the postmaster general on Saturday, saying changes under his purview have undercut the Postal Service and threatened the ability of Americans to vote.

About 100 people gathered in the wealthy residential neighborhood of Kalorama outside the apartment complex of the postmaster general, Louis DeJoy, a Republican megadonor and ally of President Trump who was appointed in May. Videos on social media showed them banging spoons on pots, blaring horns and chanting “resign,” with many in the group wearing masks and remaining socially distanced.

Critics say that changes enacted under Mr. DeJoy’s oversight, like cutting overtime pay for postal workers and removing mail-sorting machines, have slowed the delivery of mail and endangered vote-by-mail operations when millions of people are expected to exercise that option because of the coronavirus pandemic.

The Postal Service sent letters in July to all 50 states and the District of Columbia cautioning them that it may not be able to meet their deadlines for delivering last-minute mail-in ballots. News reports about the letters on Friday intensified the criticism directed at the Postal Service and Mr. Trump by Democrats and voting rights advocates, who say the president is deliberately stoking unfounded concerns that voting by mail will lead to fraud and miscounts as a way to cast doubt about the outcome of the election.

In the letters, Thomas J. Marshall, the general counsel for the Postal Service, urged states to require that residents request ballots at least 15 days before an election — rather than the shorter periods currently allowed under the laws of many states.

He said 45 states faced the risk that their timetables could leave some voters unable to get their ballots postmarked by Election Day or received by election boards in time to be counted.

In response to the warning letters, some states, including Pennsylvania and Michigan, have called for extensions on counting late-arriving ballots in the November election.

Mr. DeJoy, who has argued he is modernizing the Postal Service to make it more efficient, has become a target of criticism. Posts on social media showed protesters delivering fake absentee ballots to the entrance of Mr. DeJoy’s building on Saturday, cluttering the glass front doors with folded sheets of paper that read, “Save the post office. Save our democracy.”

The protests were organized by Shut Down D.C., a group that has previously organized in response to climate change and public health crises. In a statement, the group accused Mr. DeJoy of gutting “the safest and most accessible way to vote” in the United States.

President Trump will travel to the battleground state of Pennsylvania on Thursday to deliver remarks attacking Joseph R. Biden Jr. just a few miles from the former vice president’s childhood home, a few hours before Mr. Biden is scheduled to take the stage at the Democratic National Convention.

The Trump campaign said Saturday that Mr. Trump will discuss “Joe Biden’s record of failure” in remarks he will deliver in Old Forge, Pa., roughly six miles southwest of Scranton, Pa., where Mr. Biden grew up. He will offer his comments around 3 p.m. on Thursday, the campaign said.

A spokesman for Mr. Biden on Saturday called Mr. Trump’s event a “sideshow” and “a pathetic attempt to distract from the fact that Trump’s presidency stands for nothing but crises, lies and division.”

Mr. Biden is scheduled to accept the Democratic nomination on the last day of the party’s online convention and deliver his own speech Thursday night around 10 p.m.

Mr. Trump’s planned stop in Pennsylvania on Thursday will cap a week in which he is scheduled to swing through Minnesota, Wisconsin and Arizona — all states that could also be potentially up for grabs in the fall — and attack Mr. Biden on the economy and immigration during a key week for Democrats.

Vice President Mike Pence is also scheduled to travel to Wisconsin on Wednesday, where the Trump campaign said he will criticize Mr. Biden over his record on taxes and trade.

In addition to featuring remarks by Mr. Biden and his running mate, Senator Kamala Harris of California, the Democratic National Convention will feature prime-time keynote speeches by Michelle Obama on Monday, Jill Biden on Tuesday and Barack Obama on Wednesday.

The Trump campaign is launching an aggressive four-day digital advertising campaign that will take over some of the internet’s most conspicuous real estate during the three marquee days of the Democratic National Convention — a nearly all-digital event.

Adhering to the president’s penchant for focusing attention on himself during major Democratic events, the Trump campaign will be taking over the banner of YouTube for 96 hours starting on Tuesday, the second day of the convention, an expensive and far-reaching digital gambit.

The campaign will also blanket the home pages of The Wall Street Journal, The Washington Post and FoxNews.com with Trump campaign ads. Even non-convention programming will be inundated with Trump ads, as the campaign has bought premium, or “unskippable,” ads on sites like Hulu.

The campaign amounts to “high-seven figures,” a significant sum to spend online in such a short period of time, and could top $10 million (a few digital ads are sometimes charged extra based on engagement). The takeover of the YouTube banner and the news sites’ home pages are national buys, while the spending for Hulu and others will be in swing states.

Trump campaign officials said they were able to grab the digital slots because the Democrats, who moved their original convention date, had not purchased the time for the original week in July, nor for the new one beginning on Monday.

As Joseph R. Biden Jr. announced that he had selected Kamala Harris of California as his vice-presidential running mate, internet trolls got to work.

Since then, false and misleading information about Ms. Harris has spiked online and on TV. The activity has jumped from two dozen mentions per hour during a recent week to over 3,200 per hour in the last few days, according to the media insights company Zignal Labs, which analyzed global television broadcasts and social media.

Much of that rise is fueled by fervent supporters of President Trump and adherents of the extremist conspiracy movement QAnon, as well as by the far left, according to a New York Times analysis of the most widespread falsehoods about Ms. Harris. On Thursday, Mr. Trump himself encouraged one of the most persistent falsehoods, a racist conspiracy theory that Ms. Harris is not eligible for the vice presidency or presidency because her parents were immigrants.

“Sadly, this wave of misinformation was predictable and inevitable,” said Melissa Ryan, chief executive of Card Strategies, a consulting firm that researches disinformation.

Many of the narratives are inaccurate accusations that first surged last year during Ms. Harris’s campaign to become the Democratic presidential nominee.

A Democratic congressman from New Jersey is asking the state’s attorney general to open a criminal inquiry into what he calls President Trump’s attempts to sabotage the election by undermining the United States Postal Service.

In a letter on Friday, the congressman, Bill Pascrell Jr., pointed to slowdowns in mail delivery, the removal of mail-sorting machines and Mr. Trump’s statement this week that he opposed Democratic demands for additional funding for the Postal Service and election security because of his opposition to mail-in voting.

Mr. Trump’s actions threaten the plans, announced Friday by New Jersey’s governor, Philip D. Murphy, to conduct the upcoming general election almost entirely with mail-in ballots to protect poll workers and voters from the coronavirus, Mr. Pascrell wrote in the letter to New Jersey’s attorney general, Gurbir S. Grewal.

“I call upon you to open a wide-ranging investigation of Trump’s actions to interfere in our elections and to empanel a grand jury for the purpose of considering criminal indictments for Donald Trump, U.S. Postmaster General Louis DeJoy, members of the United States Postal Service (USPS) Board of Governors, and any other officials in the Trump government that are participating in or have participated in the subversion of New Jersey state elections,” Mr. Pascrell wrote.

A spokesman for Mr. Grewal, a Democrat, said that the attorney general was “deeply concerned by recent reports of potential political interference in the operations of the U.S. Postal Service.”

“As is our standard practice, we are neither going to confirm nor deny a grand jury investigation,” said the spokesman, Steven Barnes.

Joseph R. Biden Jr.’s choice of Ms. Harris as his running mate has been celebrated as a milestone because she is the first Black woman and the first of Indian descent in American history to be on a major party’s presidential ticket.

But her selection also highlights a remarkable shift in this country: the rise of a new wave of children of immigrants, or second-generation Americans, as a growing political and cultural force, different from any that has come before.

Ms. Harris’s parents — who arrived in the United States in the late 1950s and early 1960s as graduate students originally from India and Jamaica — were at the leading edge of a historic wave of immigration from outside Europe that would transform the United States in ways its leaders never imagined.

At 55, Ms. Harris is on the older side of this second generation of Americans whose parents came in those early years. But her family is part of a larger trend that has broad implications for the country’s identity.

The immigrants who arrived about 50 years ago — people from countries like India, China and Korea — often had higher education, but rarely went into politics. Their children, now middle-aged adults, are the ones moving into American public life.

“When my parents came, it was like, ‘we just want to make it,’” said Suhas Subramanyam, who was born to Indian parents in Houston in the 1980s, and in 2019 became the first Indian-American to be elected to the Virginia House of Delegates. “But the second generation, we want to make our mark on the world. I wanted to do more than just work at a law firm and make money. I feel very patriotic about America.”

The Postal Service’s inspector general said Friday she had opened an investigation into complaints that leading Democrats have filed against the postmaster general, Louis DeJoy, a Republican megadonor and ally of President Trump, who has begun a series of cuts to the agency that Democrats say have slowed down the delivery of mail and endanger vote-by-mail operations.

“We are in receipt of the congressional request and are conducting a body of work to address concerns raised,” a spokeswoman for the U.S. Postal Service inspector general, Tammy L. Whitcomb, said.

Senator Elizabeth Warren, Democrat of Massachusetts, Representative Carolyn Maloney, Democrat of New York and others last week requested the inspector general investigate “all recent staffing and policy changes put in place” by Mr. DeJoy.

“We have to see the blatant attacks on our Postal Service from Donald Trump and Louis DeJoy for what they are: An attempt to silence the people and undermine our democracy,” Ms. Warren wrote on Twitter.

She said the inspector general was “investigating all aspects of our request,” adding: “I’ll keep using every in the toolbox to stop Trump & DeJoy from sabotaging the USPS.”

Mr. DeJoy has argued that he is modernizing the money-losing agency to make it more efficient. Among his moves have been cuts to overtime for postal workers, restrictions on transportation and the reduction of the quantity and use of mail-processing equipment.

In a typical summer, hundreds of thousands of car enthusiasts would have traveled to metro Detroit this weekend for the annual Woodward Dream Cruise.

But the throwback event on Woodward Avenue, which connects Detroit to its northern suburbs, was canceled this year because of Covid-19. Thousands still showed up on a sultry Saturday afternoon to show off their cars and for many, their support for President Trump.

For James Stirnemann, 77, of Rochester, the cruise was familiar territory. He’s been showing off his 1957 Cadillac 62 Series convertible for years at the Dream Cruise. While he wouldn’t mar the mint-condition car with a bumper sticker or flag, his support for Mr. Trump was strong.

“He’s done more than any president that I’ve ever known,” he said.

For Patricia Jessup, 65, of Bloomfield Hills, standing alongside the avenue waving a Trump sign with so many other supporters was liberating.

“There are so many Trump supporters who are afraid to say that they support the president,” she said. “With all these people out here, you feel more comfortable showing your support too.”

A block away, a couple dozen opponents of Mr. Trump held their own rally with signs supporting the Black Lives Matters movement and a few more profane sentiments about the president. The two groups briefly scuffled in the middle and there was one arrest, said Bloomfield Township Police Sgt. Peter Matejcik.

President Trump’s re-election campaign has spent tens of millions of dollars on television ads attacking his Democratic opponent, Joseph R. Biden Jr. While their content varies greatly, the tactics used remain constant: selectively edited remarks and exaggerations.

The New York Times reviewed 22 ads from the Trump campaign that have aired since June and that have been tracked by Advertising Analytics. We found that 14 of those ads contained clearly misleading claims or videos. Here’s are some examples.

• Exaggerations about criminal justice issues: Throughout much of June and July, the ads focused on activists’ calls to defund the police, with hyperbolic warnings about the ramifications. Two spots featured people calling 911 only to be connected to voice recordings saying no one is there to answer their call, with one spot claiming “violent crime has exploded.” But that’s largely false. Compared with the same time period last year, violent crime and property crime have decreased through June in large American cities this year, though murders have increased.

• Distorting Mr. Biden’s positions: Several Trump campaign ads take comments Mr. Biden has made out of context to falsely claim he supports defunding the police, heavily raising taxes on middle-class families and eliminating charter schools. The former vice president has repeatedly said that he does not support calls to defund the police entirely, but that federal grants to police departments should incentivize reform efforts and best practices while specific decisions about funding should be made at a local level. He supports continuing federal funding for high-performing public charter schools, and while his tax proposals would generate an additional $4 trillion in federal revenue over the next decade, the wealthiest top 1 percent of taxpayers would bear about three-quarters of tax increases.

• Personal attacks through deceptive editing: The Trump campaign has taken shots at Mr. Biden’s mental acuity through deceptively edited videos and images. One ad and its Spanish version call Mr. Biden “clearly diminished” and include a clip of Mr. Biden saying, “Sometimes I wake up and think it’s 1920.”

  While Mr. Biden has been prone to gaffes on the campaign trail, that specific comment is not an example of one. Rather, it is how Mr. Biden has occasionally expressed dismay over the current social and political atmosphere. “Some mornings that I wake up, I wonder whether or not we are living in 2020 or 1920,” he said in January in Texas. “I hear the voices of intolerance singing the chorus of hate, intolerance.”

A union representing tens of thousands of New York City police officers endorsed President Trump for re-election on Friday, citing what leaders said was Mr. Trump’s defense of the authorities and concern for public safety at a time they said their members have been “under attack.”

At a rally held at Mr. Trump’s golf club in Bedminster, N.J., and attended by roughly 100 people, the head of the Police Benevolent Association, which represents about 24,000 rank-and-file officers, said he could not remember another time the union had endorsed a candidate for president.

“Across this country, police officers are under attack. Our neighborhoods are being ripped apart by violence and lawlessness,” Patrick J. Lynch, the union president, said in a statement released by the Trump campaign, which echoed rhetoric often espoused by Mr. Trump. “Most politicians have abandoned us, but we still have one strong voice speaking up in our defense.”

Mr. Trump has pushed a “law and order” message, insisting that crime will surge if voters elect Joseph R. Biden Jr. His campaign ads have also falsely claimed that Mr. Biden supports defunding the police, which Mr. Biden has repeatedly said he opposes.

Mr. Trump also delivered remarks at the event, admonishing protesters who have clashed with the authorities over police killings of Black people, according to pool reports.