Three weeks after a debate spectacle defined by heckling and sharply personal attacks, Joseph R. Biden Jr. and President Trump will meet again on Thursday in the last major prime-time opportunity for Mr. Trump to try to change the trajectory of the race before Election Day.
Republicans would like to see the president offer an affirmative vision for the country and draw policy contrasts with Mr. Biden in terms that resonate with the few undecided voters remaining. But Mr. Trump, with his history of indiscipline and invective, has struggled to define Mr. Biden this year — and he is running short on time.
The debate comes 12 days before Election Day, as many Americans have already cast ballots, and as polls show the president trailing nationally and confronting close races even in states he won handily four years ago.
Mr. Trump’s advisers hope that he can get under Mr. Biden’s skin on Thursday at the debate in Nashville, which will begin at 9 p.m. Eastern. But they have also urged the president not to interrupt Mr. Biden repeatedly, after a first contest in which Mr. Trump constantly hectored his rival — and Mr. Biden told him to “shut up” — as the evening spiraled out of the moderator’s control.
The president has signaled he intends to focus on Mr. Biden’s son Hunter and his business dealings, after an unsubstantiated New York Post report on that subject. But some advisers fear he will not be able to control himself and will attack the younger Mr. Biden in a way that engenders sympathy for the Biden family, a dynamic that unfolded in the first debate when Mr. Trump mocked Hunter Biden’s history of battling drug addiction.
“The president, in order to have a successful debate, has to go on offense without being offensive,” said Brett O’Donnell, a Republican strategist who has coached candidates in debates. “The American people care more about their own family than they do about the family of Hunter Biden. Especially during the pandemic.”
Mr. Trump has spent days attacking the Commission on Presidential Debates, which organizes the events and announced this week that the microphones of both candidates would be muted at times, as well as the moderators the commission has chosen. In an interview with “Fox and Friends” on Tuesday morning, the president continued along that path, but suggested he was listening to his advisers for now.
“They said if you let him talk, he’ll lose his chain of thought,” Mr. Trump said. “But I also understand that as he’s going down the line and issuing lies, you know, generally it’s OK to, you know, really attack that.”
Mr. Biden, for his part, is working to protect his advantage by relying on arguments that have defined his pitch for months: that he is the candidate best equipped to lead the nation out of the pandemic and its attendant economic fallout, and that he can restore stability and a measure of civility to the office after Mr. Trump’s turbulent tenure. He and his team, though, are bracing for ugly attacks, and some allies hope that the candidate, who is fiercely protective of his children, will avoid growing so angry onstage that he appears rattled.
The Democratic nominee may also be pressed on a number of issues he has struggled to crisply address in the past. In particular, allies expect that he will face questioning on expanding the Supreme Court, a matter he has repeatedly dodged, though he has said that he will clarify his position before Election Day.
“He’s going to be asked about the Supreme Court, and Trump will try to goad him about Hunter,” predicted John Morgan, an early Biden donor. “Because Trump knows that Joe Biden’s family is his hottest hot button.”
As of Wednesday morning, Mr. Trump had two tentative, one-hour sessions on his schedule for some form of debate prep before Thursday night. But some advisers were skeptical that much would be accomplished, especially with such a reduced time frame. The debate prep sessions, such as they are, are expected to include different advisers from those who were involved before the first debate. Aides have also been preparing notes for him with subject matter he should raise, or be prepared for.
Last week, Trump advisers tried gently suggesting, as they prepared him for his NBC town hall event with Savannah Guthrie, that he needed to be more controlled and less caustic than in the first debate. Aides claim he has processed that information, though he was combative and refused to disavow a conspiracy theory movement during the first part of that appearance, too. But his behavior in the second half of the town hall, during which he answered policy questions without attacking Ms. Guthrie, is what advisers hope to see from him on Thursday night.
Mr. O’Donnell, the Republican strategist, suggested that Mr. Trump’s frequent interruptions in the previous debate prevented viewers from absorbing some of Mr. Biden’s shakier responses.
“I don’t think either one of them did a good job in the debate,” he said, “because the president was so over the top he didn’t get a chance to have that contrast where Joe Biden gets mad or frustrated.”
The president’s advisers have also gone over with him his third debate against Hillary Clinton in 2016, which they believe was his best of the three he had in that campaign, in part because he was relatively articulate while being specific in discussing policies, despite the moment when Mrs. Clinton called him a “puppet” of Russia and his response was: “No puppet, no puppet. You’re the puppet.”
“I would be coaching the president to separate the things that get applause at rallies of committed Trump supporters from the things undecided voters want to hear,” said Brad Todd, a Republican strategist. “He does need to communicate to swing voters that the real stakes in this election are not the past, not even the present, but they are the future, of rebuilding the economy.”
Mr. Biden and his allies are skeptical that Mr. Trump will confine his remarks to such subjects.
“I wish I had a dollar for every time we’ve heard Donald Trump’s advisers are signaling some calming behavioral change,” said Hilary Rosen, a Democratic strategist close to the Biden team.
Mr. Biden, a fan of briefing books and of intense preparation even for lower-key appearances, has largely stayed off the campaign trail this week, getting ready for Thursday’s matchup.
His preparation is guided by a group of close allies including Ron Klain, a former Biden chief of staff and veteran of presidential debate prep; Steve Ricchetti, a longtime adviser; Mike Donilon, the candidate’s chief strategist; Anita Dunn, a senior adviser who was spotted with Mr. Biden in his hometown, Wilmington, Del., this week; and Bob Bauer, a former White House counsel.
Other senior officials involved include Stef Feldman, Mr. Biden’s policy director; Kate Bedingfield, his communications director and a deputy campaign manager; Symone Sanders, a senior adviser; and two top policy advisers, Jake Sullivan and Antony J. Blinken.
Mr. Biden’s advisers see the race as a referendum on Mr. Trump’s leadership during the pandemic, and they view the debate as another chance to highlight differences with the president as coronavirus cases rise across the country — indeed, Mr. Trump and many of his advisers said after the first debate that they had tested positive, and the president was hospitalized for several days.
Mr. Biden is expected to highlight his own plans around health care and reviving the economy in a week when Mr. Trump has sharply criticized Dr. Anthony S. Fauci, the nation’s top infectious disease expert. The former vice president’s team has also signaled that it will cast personal attacks as an attempted diversion from the most urgent issues facing the nation. And some close to the Biden campaign have pointed to polls that showed a backlash to Mr. Trump’s first debate performance and his sharp personal attacks.
“When Donald Trump obsesses over right-wing fringe conspiracy theories, he merely reinforces what we’ve said the whole time: that he’s forced to run away from his own record” on the pandemic and the economy, said Andrew Bates, a Biden spokesman, when asked about the possibility of attacks on Mr. Biden’s family. “If he recycles the same strategy that lost him the first debate, then he will also lose the third.”
A number of Biden allies said in interviews that there was nothing wrong with a flash of righteous anger. But they said that the wisest course was to dismiss any personal attacks by pivoting back to voters’ more tangible concerns, something Mr. Biden tried to do in the first debate by noting that many Americans have family members who struggle with addiction.
“I expect he’ll say something along the lines of, ‘This race is not about my family,’” said Jay Carney, a former White House press secretary under President Barack Obama who has also worked for Mr. Biden. “‘It’s not even about your family. It’s about all the families out there.’ Just look at the camera and take it back to the voters.”
And Mr. Biden’s running mate, Senator Kamala Harris, suggested on Wednesday that it was unlikely he would turn to attacks on Mr. Trump’s children, saying that “one of the things I love about Joe Biden” is that he does not “talk about other people’s kids,” according to a pool report.
Some Democrats argued that the best preparation for facing off against Mr. Trump was the act of debating him the first time.
“I am sure before the first debate, Joe Biden plenty of times said to his team, ‘Guys, I get it,’” said Philippe Reines, who played Mr. Trump in Mrs. Clinton’s debate prep in 2016. “Now he gets it.”