Ever since President Biden announced last year that he would run again, those in his inner circle closed ranks and brushed off the obvious question: No, they insisted, he was not too old to seek re-election.

The news media, they said, was unfairly fixated on his age. Republicans were posting wildly distorted video clips on social media making him look more feeble than he actually is. Hand-wringing Democrats fretting over the prospect of an octogenarian president turning 86 by the end of a second term were just “bed-wetters.”

Then the debate happened. And now the days of denial at the White House are over. No longer can the president’s confidants simply wave away concerns about his capacity after his unsteady performance at Thursday night’s showdown with former President Donald J. Trump. Struggling to contain a brush fire of alarm within the Democratic Party, his team is now forced to confront the issue head on.

Mr. Biden, 81, admitted himself on Friday that he is no longer a young man and that he has lost a step debating, even as he made a more forceful case for himself at an energized rally in Raleigh, N.C., than he had on the debate stage in Atlanta the night before. The Biden team seized on validation from Democratic allies like former President Barack Obama and Representative James E. Clyburn of South Carolina to reject calls on the president to cede the nomination to a younger candidate.

But many distressed Democrats, including some in his own administration, were left wondering how it had come to this and, fairly or not, faulted the president’s team for letting it happen: How could those closest to Mr. Biden not have talked him out of running? How could they have agreed to debate knowing that he might stumble so badly? How could they not have prepared him better for the predictable challenges during a week hidden away at Camp David?

“Last night was kind of shocking because we’d heard they’d been preparing and so on,” David Axelrod, who was a senior adviser to Mr. Obama, said the morning after the debate. “And the first 10 minutes were a disaster, and it’s hard to understand how that happened.” As it turned out, he added, “this was a great opportunity to allay people’s concerns and it had the opposite effect.”