President Biden has told a key ally that he knows he may not be able to salvage his candidacy if he cannot convince the public in the coming days that he is up for the job after a disastrous debate performance last week.

The president, who the ally emphasized is still deeply in the fight for re-election, understands that his next few appearances heading into the holiday weekend — including an interview scheduled for Friday with George Stephanopoulos of ABC News and campaign stops in Pennsylvania and Wisconsin — must go well.

“He knows if he has two more events like that, we’re in a different place” by the end of the weekend, said the ally, referring to Mr. Biden’s halting and unfocused performance in the debate. The person spoke on the condition of anonymity to discuss a sensitive situation.

The conversation is the first indication to become public that the president is seriously considering whether he can recover after a devastating performance on the debate stage in Atlanta on Thursday. Concerns are mounting about his viability as a candidate and whether he could serve as president for another four years.

A top adviser to Mr. Biden, who also spoke on the condition of anonymity to discuss the situation, said the president was “well aware of the political challenge he faces.”

White House officials did not immediately respond to a request for comment.

Campaign officials were nervously watching polls, recognizing that bad numbers could fuel the crisis. A CBS News poll on Wednesday showed former President Donald J. Trump edging ahead of Mr. Biden since the debate with 50 percent to 48 percent nationally and 51 percent to 48 percent in battleground states.

Mr. Biden is slowly reaching out to Democratic elected officials and has a meeting with Democratic governors at the White House scheduled for Wednesday evening. He is also continuing to reach out to people he has long trusted and has told at least one person that he is open to the possibility that his plans to move on from his debate performance — and flip the focus back to his challenger, Mr. Trump — may not work.

Several allies of Mr. Biden, who has huddled with the family and advisers since the debate on Thursday, have underscored that the president is still in the fight of his political life and largely sees this moment as a chance to come back from being counted out, as he has done many times throughout his half-century career.

But he is also cleareyed, they said, about his uphill battle to convince voters, donors and the political class that his debate performance was an anomaly.