BILLINGS, Mont. — President Trump tried on Thursday to tamp down perceptions of an out-of-control White House, after a string of devastating reports about his insurgent staff, warning supporters here that if they did not turn out to vote in November, his political enemies would subject him to impeachment.

“If it happens, it’s your fault because you didn’t go out to vote,” Mr. Trump said to an enthusiastic rally in a state he won comfortably in 2016. His impeachment at the hands of a Democratic majority, he said, would turn the United States into “a third-world country,” where the opposition routinely impeaches the sitting leader.

Speaking to a friendly crowd during one of the most chaotic stretches of his presidency, Mr. Trump also turned his fire on the news media, accusing it of ignoring his successes and waging a campaign to delegitimize him.

“The truth is, with these people, you can’t win.” But he insisted, “I’m winning.”

Nearly 2,000 miles away in Washington, Mr. Trump had been confronted by an extraordinary anonymous Op-Ed essay published in The New York Times and a new book by Bob Woodward, both of which depicted a “quiet resistance” of aides standing up against the president.