President Trump won the White House in no small part by seizing on Hillary Clinton’s missteps and using them to turn many voters against her. But after three unsteady months, and with the Republican convention six weeks away, Mr. Trump is struggling to define Joseph R. Biden Jr. to similarly devastating effect, a critical task at this stage of a presidential race.

By a combination of design and circumstance, Mr. Biden, the presumptive Democratic nominee, has managed so far to deny Mr. Trump the sort of damaging offhand remarks, campaign clashes and clumsy encounters with voters that he used as weapons against Mrs. Clinton in the last general election, as well as his Republican opponents in the 2016 primary.

This is partly because Mr. Biden has run such a low-profile campaign during the pandemic. He has had few public appearances and news conferences, which can provide the unscripted moments’ opponents can use to shape the public’s perception of a candidate.

But there are other obstacles for Mr. Trump that have become clear since Mr. Biden effectively won his party’s nomination in April. Mr. Biden, the former vice president, is viewed more favorably by voters than Mrs. Clinton was in 2016. He is a moderate Democrat who lacks a history of harsh partisanship or scandal. And he has long appealed to white working-class voters, who are part of Mr. Trump’s base.

“It is going to be more difficult for the Trump campaign to go after a man who really is a centrist, has dealings with people across the aisle and knows how to talk to people who disagree with him,” said Priscilla Southwell, a professor emerita of political science at the University of Oregon. “And 2020 is a different kind of year. Donald Trump can appeal to his core by being negative, but it’s such a difficult time for everybody. I don’t think negativity is going to sell as well as it used to.”

Defining an opponent — putting them on the defensive with caricature — is a crucial and proven tactic for candidates in competitive races. There is a graveyard of failed contenders — names like Kennedy, McGovern, Romney, Gore, and Hillary Clinton — who found themselves branded by an opponent in portrayals, often unfair, that ricocheted across the political playing field and the media.

Mr. Trump had been adept at this. But the kind of attacks that seemed so effective when he was a new-to-politics outsider in 2016 also appears to have less resonance coming from inside the White House. Four years of tweets by Mr. Trump have numbed many voters.

“It’s almost self-defeating,” said Ron Christie, a Republican who was a senior adviser to President George W. Bush and Vice President Dick Cheney. “People are exhausted. The president, with every tweet, every insult, will move out of favor with the demographic that he needs the most, which is the independent.”

Mr. Trump does have some avenues to use against Mr. Biden before voter attitudes begin to harden. He has sought to tie Mr. Biden to the political unrest that has swept the country since the killing of George Floyd in Minneapolis on May 25 by the police. And Mr. Trump has tried to portray his opponent as senile, “sleepy,” corrupt, and an ally of China, but none of those lines of attack has resonated with the public, at least up to now.

His aides have signaled that Mr. Trump, incumbent or not, would run as an outsider against Mr. Biden — who has been a fixture in Washington since he was elected to the Senate in 1972 — the way he had against Mrs. Clinton. Mr. Biden’s long history of votes in the Senate, as well as his eight years as an active vice president under President Barack Obama, could give Mr. Trump plenty of material.

And if Mr. Biden continues to escape definition, Mr. Trump is likely to turn to Mr. Biden’s running mate. Going after the vice-presidential candidate would be an unusual but not unprecedented strategy, and might have some resonance in this election given Mr. Biden’s age; he is 77. (Mr. Trump is 74.)

Mr. Trump’s campaign had calculated that Mr. Biden, given his long history and the stumbles in the early days of his primary, would be an easier opponent to caricature.

But now time is running short. A series of national polls have shown Mr. Trump trailing Mr. Biden, often by double digits. Even more alarming for the president, he is trailing Mr. Biden in battleground states that he won in 2016 and are likely critical to any re-election plan — including Wisconsin and Pennsylvania. Even states like Georgia, which once seemed clearly in Mr. Trump’s column, now appear competitive.

“Trump has much less time to pile up negatives on Biden,” said Nelson Warfield, a Republican consultant who served as press secretary for Bob Dole’s presidential campaign in 1996. “I made my first negative ad starring Hillary Clinton in 1992 and I kept doing ads criticizing her across the next 24 years. And I was by no means alone. Republicans have months to do to Biden what Republicans had over two decades to do to Hillary.”

Mr. Trump would certainly seem to have a few advantages here to make his case. He has the platform of the White House and his Twitter account. Until two months ago, he enjoyed a huge financial advantage over Mr. Biden. And Mr. Trump, unlike Mr. Biden, never had to worry this year about a primary or uniting his party behind him.

But to the frustration of Republicans, his attempts to define Mr. Biden have seemed fitful. He barely mentioned Mr. Biden during two of his campaign’s highest-profile moments in months: his speech in front of Mount Rushmore last week, followed by his July 4 address from the White House South Lawn.

And when Mr. Biden has made mistakes, Mr. Trump’s campaign has struggled to turn them to its advantage. When Mr. Biden said that any African-American voter who considered supporting Mr. Trump “ain’t Black,” the Trump campaign roared into action, but the fallout lasted only a day, particularly after Mr. Biden apologized.

While Mr. Trump has filled the space on the stage that Mr. Biden has left open, he has been the one to make campaign missteps that provided fodder for Democrats, notably when he said at a rally that given the increase in positive tests for Covid-19, “I said to my people, ‘Slow the testing down, please.’”

Mr. Trump has the obstacle of familiarity in trying to draw attention to his attacks. And his credibility has suffered over these past four years, which might make him an imperfect messenger to go after Mr. Biden: 67 percent of voters in a New York Times/Siena College poll last month said they think Mr. Trump promotes falsehoods or conspiracies very or somewhat often.

“The truth is people have heard him mocking and demonizing for four years now,” said Mark Mellman, a Democratic pollster. “They are somewhat inured to it, they are sick and tired of it. And by being home, Biden has given him less to shoot at.”

The period before the conventions is typically the time when candidates make the kind of mistakes their opponents can use to set the frame for the fall campaign.

Mr. Trump’s campaign pounced when Mrs. Clinton was taped saying half of Mr. Trump’s supporters were a “basket of deplorables.” Mitt Romney, the Republican presidential candidate in 2012, was caught at a private fund-raiser saying 47 percent of Americans were “people who pay no income tax” and were “dependent upon government.”

John F. Kerry, as the Democratic presidential candidate in 2004, was caught on video windsurfing back and forth across the Nantucket Sound. That provided the perfect image for an attack advertisement by President George W. Bush, which portrayed him as a flip-flopper, his policy positions changing with “whichever way the wind blows,” as the announcer put it. (In the process, the advertisement underlined the Bush campaign’s effort to portray Mr. Kerry as elite.)

In Mrs. Clinton, Mr. Trump had an unpopular opponent easy to demonize. In the final month before Election Day, 54 percent of respondents had an unfavorable view of her, according to a New York Times/CBS News Poll. Mr. Trump was in similar straits; he was viewed unfavorably by 56 percent of voters, the same percentage he holds today, according to the recent Times/Siena poll.

Mr. Biden, on the other hand, was viewed unfavorably by just 42 percent of voters in the same poll; 52 percent viewed him favorably.

“That was what was historic about that race,” said Joel Benenson, who was chief strategist for Mrs. Clinton. “You don’t have that now. You have Trump with that high unfavorable rating. But Biden doesn’t have that.”

“And he’s the president now,” Mr. Benenson said. “He ran as a bomb-throwing presidential candidate. He could throw it at any candidate, they were the establishment. He owns it now.”

Ms. Southwell said that Mr. Biden presented a different kind of target than Mrs. Clinton. “It’s not that he hasn’t been an insider,” she said. “He’s had a different kind of upbringing and a different kind of career than Hillary Clinton.”

In many ways, Mr. Biden has turned the tables on Mr. Trump: He is running as if he were the incumbent, while Mr. Trump is acting like the challenger. The question is whether he will be able to maintain that posture through the election.

“Biden’s basement Rose Garden strategy has enabled him to play the role of a generic Democratic candidate, without the microscopic scrutiny that he would otherwise have been subjected to,” said Neil Newhouse, a Republican pollster who worked for Mr. Romney. “Joe Biden is not Hillary Clinton, in that he doesn’t have the built-in negatives that Hillary embodied. So, while Americans can absolutely still define Biden, they have significantly less time to do so.”

By Sanjida Jannat