The country has seen this version of President Biden before, the grimly determined politician trying to project self-confidence, even cockiness. It is the chip-on-his-shoulder Biden, the one who likes to pointedly remind everyone that he has proved his detractors wrong before and vows to do it again.

A week after his disastrous debate performance and amid rising doubts inside his party about his capacity to defeat former president Donald Trump in November, Biden has adopted a one-word strategy to keep his candidacy alive: defiance.

Many Democrats believe instead that he is in denial.

Whatever private thoughts he may have about his current plight to the contrary, his public-facing persona is one of grim determination. He shows no patience for the doubters and the whiners and the critics who, after watching him falter before 50 million viewers of the debate, wonder if he has the mental sharpness and physical strength to keep Trump out of the White House, much less serve another four years as president.

Biden is dismissive of those who want him out, almost daring them to come from behind their anonymous quotes in the press and make their case publicly, with their names attached. A few of them have, but Biden insists that they represent a small fraction of his party.

This was the Biden on display on Friday. At a rally in Madison, where he delivered a fiery speech, he threw down the gauntlet. He pointed to the Atlanta debate, where he struggled with his words, missed opportunities to make his case against Trump and at points appeared to have fully lost his train of thought.

“Ever since then,” he said, “there’s been a lot of speculation. ‘What’s Joe going to do? Is he going to stay in the race? Is he going to drop out?’ Well, here’s my answer: I am running, and I’m going to win again!”

Later, in an interview with ABC’s George Stephanopoulos that aired in prime time Friday night, he was pressed repeatedly about what he would do if leaders of his party came to him and said he should get out. He called it a hypothetical question and refused to engage.

He said he has talked with House Democratic Leader Hakeem Jeffries (N.Y.), whose members wonder if Biden will ruin their hopes of winning back the majority; Senate Democratic Leader Charles E. Schumer (N.Y.), who is in danger of seeing Republicans claim the majority in his chamber; and Rep. James E. Clyburn (D-S.C.), who saved his candidacy during the 2020 primaries but who has also indicated he would support Vice President Harris if Biden were to step aside.

“They all said I should stay in the race,” Biden told Stephanopoulos.

Biden said the Democratic governors are all for him. After all, he said, he met with them on Wednesday and they’re all behind him. But that overstates the degree of unanimity among the governors.

Earlier Friday, Massachusetts Gov. Maura Healey put out a statement saying that Biden should “carefully evaluate whether he remains our best hope to defeat Donald Trump.” Other governors have been reluctant to go public but have indicated privately that they share Healy’s view. And in Wednesday’s meeting, for instance, New Mexico Gov. Michelle Lujan Grisham and Maine Gov. Janet Mills reportedly told Biden that they were worried that he might lose their states, which were solidly in Biden’s column four years ago.

Asked on the tarmac in Wisconsin about a report in The Washington Post that Sen. Mark R. Warner (D-Va.) has been trying to assemble a group of senators to go to him and urge him to get out, Biden told reporters, “He’s the only one.” That assertion overlooks the private worries senators have been sharing with one another. Over in the House, meanwhile, several Democrats have publicly called for Biden to withdraw.

What or who might persuade the president to see things differently? Biden had an answer for that in his ABC interview: “If the Lord Almighty came down and said, ‘Joe, get out of the race,’ I’d get out of the race,” he said. And then he added, “The Lord Almighty’s not coming down.”

Multiple news organizations, including The Post, have published stories recently that have quoted people who have been in meetings with him and who say they have seen signs of accelerated aging in recent months, including more common lapses. Few quotations were on the record, other than those from administration officials who were offered to reporters by the White House to vouch for the president’s fitness.

Pressed repeatedly by Stephanopoulos about his willingness to take a cognitive test, Biden declined to answer definitively. “I have a cognitive test every day,” he said, alluding to the rigors of being president. “Every day I have that test. Everything I do. You know, not only am I campaigning, but I’m running the world.” He amended that to say the United States is the world’s “essential” nation.

Biden called on the voters who made him the Democratic nominee during the primaries earlier this year not to let strategists, donors and unnamed party officials convince them to deny him what they gave him. “Despite that, some folks don’t seem to care who you voted for. Well, guess what? They’re trying to push me out of the race. Well, let me say this as clearly as I can: I’m staying in the race. I’ll beat Donald Trump.”

But voters who have not seen him up close or in private meetings nonetheless have concluded that he is not fit to serve another four years in the White House. A Wall Street Journal poll published on Wednesday found that 76 percent of Democrats think he is too old to run. About 2 in 3 say they would prefer another Democrat as their nominee. A New York Times/Siena College poll found that 74 percent of voters overall said he is too old, including 59 percent of Democrats.

Speaking with Stephanopoulos, the president appeared to be in denial about the state of the race, especially compared with his standing at this point four years ago. David Axelrod, the Democratic strategist, posted on X: “The president is rightfully proud of his record. But he is dangerously out-of-touch with the concerns people have about his capacities moving forward and his standing in this race.”

Today he trails Trump narrowly in national polls and his position is slightly worse than before the debate. Those polls measure the popular vote. His standing in battleground states, which will determine who wins in the electoral college, has generally been worse.

Four years ago, Biden consistently led Trump in national polls. A Washington Post-ABC News poll in mid-July 2020 showed Biden leading Trump 55 percent to 40 percent. He went on to win by four percentage points and 7 million votes nationally. Biden won 306 electoral votes, solidly surpassing the 270 needed to win, but in four of the six battlegrounds he won, his margin was a percentage point or less.

The polls in 2020 consistently understated Trump’s support and pollsters have sought to improve their methodology. But by any measure, Biden is performing worse this year.

As one Democratic strategist, who served in a previous administration and who asked for anonymity to offer his candid assessment, said after watching Biden’s interview on ABC News, “He was better than the debate, but I don’t think he answered the big questions for a lot of Democrats - can he make a powerful, compelling and relentless case against Trump?”

Members of Congress, who are clearly nervous about Biden as their nominee, return to Washington next week and will be talking more among themselves about what, if anything, to do. Big donors will be deciding whether to continue to fund Biden’s campaign with no changes or scale back their contributions. More polls will be coming that could undermine - or support - the case Biden is making for himself.

Before the 2024 campaign really began, Biden stared down those questioning whether he should run again. No prominent Democrat stood up to challenge him in the primaries, despite worries about his capacity to take on Trump. Worries today are significantly greater than they were then.

Biden and the Democrats hoping he steps aside are now on a collision course. Will those who want him to go keep up the pressure, privately or publicly? Or will they shrink back in the face of Biden’s declaration that he is in the race to stay?

This has the potential to be much more contentious and divisive than the period since the debate ended. However it plays out, there are mostly risks rather than good options - and now not much time to resolve things and set a course for the final months of the campaign.