Over the course of his long career, President Biden has overcome personal tragedy and political odds, and he has used his resilience to power his ambition. But now that he is in the fight of his political life, his irrepressible pursuit of the comeback risks looking like blind defiance in the face of a rising tide.

“You’ve been wrong about everything so far,” Mr. Biden told a group of reporters who asked him on Friday why he still felt he was the best person to defeat 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 get wiped out — remember the red wave,” he said, referring to an expected wave of Republican gains that never materialized in the midterm elections. Instead, Democrats did far better than expected, a decisive factor in Mr. Biden’s decision to run for a second term.

He took that spirit with him 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 believe that’s my approval rating,” Mr. Biden said. “That’s not what our polls show.”