Resilience has fueled Biden’s career. But so has resistance.

Over the course of his long career, President Biden has overcome personal tragedy and political setbacks, using his resilience to fuel his ambition. But now that he is in the fight of his political life, his indomitable drive for a comeback risks looking like blind resistance in the face of a rising tide.

“You’ve been wrong about everything so far,” Biden told a group of reporters who asked him Friday why he still felt he was the best person to beat former President Donald J. Trump after a dismal debate performance in Atlanta plunged his campaign into crisis.

“You were wrong about 2020. You were wrong about 2022. We were going to be wiped out — think of the red wave,” he said, referring to an expected wave of Republican gains that never materialized in the midterms. Instead, Democrats fared much better than expected, a key factor in Biden’s decision to run for a second term.

He carried that spirit into a 22-minute ABC interview with George Stephanopoulos on Friday, in which he was asked about his approval rating of 36 percent.

“Well, I don’t think that’s my approval rating,” Mr. Biden said. “That’s not what our polls show.”

To rally his supporters, the president will attend several campaign rallies in Pennsylvania on Sunday with the first lady.

The comeback kid myth that Biden has built over half a century in politics is colliding with a new reality, in which he is portrayed not as a fighter who overcomes obstacles, but as a accused by his critics of putting his own ego above the country. His denial of polls, voter concerns and growing calls among Democrats to drop out of the race have left some in his party in a quandary over how aggressively to try to convince him to change course, with time running out to bring about change.

For Mr. Biden, the line “when you get knocked down, you get up” isn’t just a campaign ad. It’s a key to understanding how he sees himself. He sees himself as the pugnacious, mainstream politician who has been consistently overlooked, underestimated, and sidelined. For him, the naysayers are as important to his story as the supporters.

And he has supporters who say they still believe in him, including Gov. Gavin Newsom, a California Democrat who visited a Biden campaign office in Pittsburgh on Friday to boost morale among volunteers in a crucial state. But even Mr. Newsom, who has been vocal about his support since Mr. Biden walked out of the debate 10 days ago, was clear about the stakes: “This is a very important week and weekend. None of us are naïve about what happens after that debate.”

Campaign officials said before the debate that Biden’s performance, good or bad, would not lead to a drop in the polls.

“This was going to be a close race anyway,” said Kevin Munoz, a campaign spokesman, “and the dynamics that are playing out now are the ones we’ve long expected: Voters are still deeply concerned about Donald Trump and his damaging agenda, and the more we reach out to voters, the more they support President Biden.”

On Saturday, Mr. Biden participated in a call with a group of senior campaign surrogates and spent an hour and 15 minutes asking for their feedback on the past few days. Senator Chris Coons of Delaware, a longtime Biden ally, said everyone on the call encouraged him to stay in the race but also indicated that supporters had a range of concerns about his ability to hold the job for another four years.

“He asked us to share, ‘Who have you heard from, who is critical or has a concern or is not convinced?’” Mr. Coons said. Mr. Biden told the group he understood the concerns and wanted to do more interviews and unscripted appearances in the future.

Kate Bedingfield, who served as White House communications director until 2023, said Biden still has to prove himself in the coming days.

“I think this is a very competitive race, but I also think there’s no question that he’s got a lot of work to do here,” Ms Bedingfield said. “This is a moment where he really needs to show people that he’s in it for the reasons that I know he’s in it for, which is to protect democracy, to defeat Donald Trump and to push back against the threat that he poses to our country.”

The ABC interview should have been a chance for him to do that. “He failed,” said David Axelrod, a veteran strategist and Obama administration alumnus. wrote in an op-ed on Saturday. People close to Mr. Biden took a different view, saying he had done enough to continue fighting an establishment that shows signs of turning on him.

On Saturday, Mr. Biden gathered with his family at his home in Wilmington, Delaware, and attended church with his sister, Valerie Biden Owens. His family has, more often than not, urged him to stay in the fight. Last week, the Bidens gathered at Camp David, where their message was again the same: Stay in. The family is still urging Mr. Biden to keep going, according to people familiar with their thinking.

Jill Biden, the first lady, has been traveling the country campaigning in recent days. Hunter Biden, Mr. Biden’s son, is pushing for his father to stay in the race.

Biden could seek advice from allies and call Democrats on Capitol Hill in an effort to prevent the dam against him from breaking, according to a half-dozen people familiar with the Biden family dynamics, but they say his decisions in the coming days and weeks will be heavily influenced by his family.

Democrats have expressed dismay in recent days that Mr. Biden’s family could have so much control over his political future, but people who know the family say it’s always been that way.

Mr. Biden said in his memoir: “Promises to keep,” that when he was considering withdrawing from the presidential primary due to a plagiarism scandal in 1987, his two sons, Beau and Hunter, caught him in the hallway at home. The couple begged him to stay in the race. They feared how much he would change if he didn’t run to prove himself and show the world who he was.

“The only thing that matters is your honor,” Hunter, then just a teenager, told his father at the time. “That’s what you always taught us. Your honor.”

“You will change, Dad,” warned his son Beau, who died in 2015. “You will never be the same.”

Mr. Biden eventually dropped out of that race, but these are different circumstances. Beau Biden is gone, and it’s a loss that has both hollowed and shaped Mr. Biden’s presidency. Hunter Biden has been convicted on three aggravated weapons charges, and his ongoing legal troubles are said to be a major personal burden for the president.

Moreover, Mr. Biden is now an 81-year-old incumbent. And Democrats closest to him still privately fear what would happen if someone other than him were on the ballot to run against Mr. Trump.

Biden has insisted his debate was a one-off and says he wants to debate Trump again. He told Stephanopoulos to pay attention when U.S. allies travel to Washington next week for a NATO meeting, where he will work to strengthen ties and hold a news conference.

“Come and listen,” Mr. Biden beckoned his interviewer, predicting the broad support he had always expected. “See what they say.”