Shortly after the 11 minutes were over and President Joseph R. Biden Jr. arose from behind the Resolute Desk in the Oval Office on the evening of July 24, he and his family filed out to the Rose Garden.

A throng of White House staff members were waiting outside, under a slight drizzle, with a faint rainbow emerging overhead. Most of them spent the preceding hour nervously eating pizza in the East Room of the White House before growing hushed to listen to their 81-year-old boss speak to the nation. Several of them had been crying earlier in the day. But midway into his speech, Biden began to enumerate his administration’s considerable legislative achievements — among them, “And we finally beat Big Pharma,” a line he had fatefully mangled in the debate with Donald J. Trump less than a month earlier, abruptly dropping the hammer on his political future. As he proceeded through these shared highlights, the tenor in the East Room seemed to change, and a few of the staff members proudly shook hands and hugged one another.

Now Biden spoke only to them, through a microphone someone handed him (according to a video of the event that I obtained). “My name is Joe Biden, and I’m Jill Biden’s husband,” he began, grinning broadly at his familiar joke, as his wife stood beside him, noticeably more subdued, working through her own emotions. “Look,” he told his aides, “the only reason that we’ve had the progress that we’ve had is because of you. And that’s not hyperbole.” He added, in a raspy but otherwise even voice: “I’m so damned proud to be a part of you. I really mean that.”

Sounding anything but deflated, Biden exhorted his staff members to think about the work there was left to do over their final six months. He wanted to extend prescription-drug benefits. He wanted to force billionaires to pay their fair share in taxes. “We can start to help lay the groundwork for Kamala,” Biden said of his vice president and now heir apparent, who was already out on the campaign trail.

He wrapped up his three minutes of remarks with a stage-whispered call to arms, as if it were a secret plan: “Let’s elect Kamala!” After their ovation, the president urged his staff to get to work on the ice cream stationed behind them. Biden cracked a few other jokes but didn’t stay for dessert. Instead, the 46th president of the United States retreated with his wife down the walkway to the residence.