The special counsel report on President Biden’s handling of classified information has led to questions about the president’s fitness to run for re-election.

Within Mr. Biden’s inner circle, no one knows how taxing the job can be more than Jill Biden, the first lady. At times, she has worked to shield him from the sort of off-the-cuff interactions with reporters that occurred on Thursday evening, when Mr. Biden veered away from scripted remarks and started answering questions.

In January 2022, after Mr. Biden held a two-hour news conference, the first lady dropped by a meeting with the president and his aides. She asked the group, which included the president, why nobody stepped in to stop it, according to a person who was in the room. Where was the person, she demanded, who was supposed to end the news conference?

Officials later apologized to her, according to an account of the episode shared by a person in the room.

“I saw Joe as V.P. and how tough that was,” Dr. Biden said in an interview at her beach home in Rehoboth Beach, Del., in the fall of 2022, referring to Mr. Biden’s eight years as vice president. “But when I see what he does, when I see the table as you get off that elevator and I see a pile like this every single night with briefing books,” she said, placing her two hands apart for emphasis, “and I see him reading and writing, it’s a lot.”

But she said it was worth the effort to stop former President Donald J. Trump from returning to office.