Contrary to his past threats, Mr. Trump said he would participate in debates in the fall after all, even though he considers the Commission on Presidential Debates biased against him. He also predicted that Representative Alexandria Ocasio-Cortez of New York would challenge Senator Chuck Schumer in a Democratic primary and “kick his ass.”

Looking ahead to his speech on Tuesday night, Mr. Trump said that Rush Limbaugh, the conservative radio host who announced on Monday that he has advanced lung cancer, may be in the audience, and the president added that he might award the broadcaster the Presidential Medal of Freedom.

He was not looking forward to having Speaker Nancy Pelosi, who orchestrated his impeachment, sitting behind him and next to Vice President Mike Pence during the speech. “There’s one person behind me who’s going to be friendly and one who’s not going to be friendly,” he said, according to the people in the room.

Mr. Trump complained at length about Mr. Bolton, whose unpublished book confirms a central allegation of the impeachment charges by reporting that the president conditioned security aid to Ukraine on its willingness to announce political investigations of former Vice President Joseph R. Biden Jr. and other Democrats.

“He turned on me,” Mr. Trump said of Mr. Bolton.

The Iowa debacle played out even as Gallup reported that Mr. Trump’s approval rating had climbed to 49 percent, its highest in that survey since his presidency began. While polls have shown that most Americans want the Senate to call witnesses, his impeachment trial is set to end Wednesday with an assured acquittal — and it is even possible, though not certain, that one or more Democratic senators vote with him.

“What other people would look at as a moment of completely political meltdown for this president, it all appears to accrue to his benefit,” said Matt Schlapp, the chairman of the American Conservative Union. “He actually looks like the adult in the room.”

Moreover, Mr. Schlapp said, the delayed count in Iowa will sow discord and suspicion within Democratic ranks. “The problem for the Democrats is it will make people think and assume the fix is in again because they don’t like who is leading,” he said.