But that spring, Mrs. Obama made it clear that she thought her husband needed a new team, according to her aides. When the president decided to deliver a lofty speech about overhauling immigration laws in June 2010, even though there was no legislation on the table and the effort could hurt vulnerable Democrats, Mr. Emanuel objected. Aides did not produce the speech he wanted and the president stayed up much of the night rewriting — but the address drew a flat reception. Mr. Obama was irritated, two advisers said, and told Ms. Jarrett to keep an eye on other top staff members to make sure that they delivered what he wanted.

Several West Wing aides said they had heard secondhand that Mrs. Obama was angry about the incident. Later, they said they wondered: was the president using his wife to convey what he felt?…

But at Mr. Emanuel’s 7:30 a.m. staff meeting the next day, Ms. Jarrett announced that the first lady had concerns about the White House’s response to the book, according to several people present. All eyes turned to Mr. Gibbs, who started to steam.

“Don’t go there, Robert, don’t do it,” Mr. Emanuel warned.

“That’s not right, I’ve been killing myself on this, where’s this coming from?” Mr. Gibbs yelled, adding expletives. He interrogated Ms. Jarrett, whose calm only seemed to frustrate him more. The two went back and forth, Ms. Jarrett unruffled, Mr. Gibbs shaking with rage. Finally, several staff members said, Mr. Gibbs cursed the first lady — colleagues stared down at the table, shocked — and stormed out.