(Mr. Schumer has proved an adept negotiator in his own right, provoking the president to claim ownership of the shutdown during an Oval Office meeting in December.)

In one sense, the row over the State of the Union reveals as much about the difficulty Mr. Trump is having adjusting to life in Washington under a divided government as it does about his treatment of women. When Paul D. Ryan, a Republican, was speaker, Mr. Trump could exert leverage over Mr. Ryan, just as he can over Senator Mitch McConnell, the Republican leader. He cannot do that with Ms. Pelosi.

Gwenda Blair, another Trump biographer, said Mr. Trump typically viewed women as “easier targets” in negotiating sessions. But that is not the case for Ms. Pelosi. For starters, the only nickname he has devised for Ms. Pelosi is her own name — Nancy.

“Nancy Pelosi, or Nancy, as I call her, doesn’t want to hear the truth,” the president told reporters Wednesday at the White House — a comment that was either meant to showcase a supposedly close relationship or, alternately, diminish her by dropping her last name. But if it was an attack, it was by Trump standards unusually restrained. (Before the election, Mr. Trump tried calling Ms. Pelosi “High Tax, High Crime Nancy Pelosi” on Twitter, but it did not stick.)

“He knows how to emasculate men and he assumes that will work, and he knows how to attempt to shame women around their appearance, but he doesn’t have a useful weapon in this relationship,” Mr. D’Antonio said. “He has yet to give her a nickname, he has yet to criticize her appearance and I think he knows that would be very risky for him to do. So I think he’s stuck in a way that he’s rarely stuck.”

John Feehery, a Republican strategist who advised former Speaker J. Dennis Hastert, sees something else at work: smart politics. He said Mr. Trump treated Ms. Pelosi respectfully for a very simple reason: He respects her.

“Compared to how he treats everybody else, I think he’s been very respectful and I think that’s good politics for him,” Mr. Feehery said, adding: “You have to be careful when you’re trying to deal with the speaker. She’s got power. You don’t want to unnecessarily insult her because that’s not good politics and I don’t think it gets him a better deal.”