Mr. Amash, friends say, is shrugging it all off. He has never really been much of a party loyalist anyway — during the midterm elections in 2018, he angered officials from the House Republicans’ campaign arm by refusing to pay his annual dues, according to a Republican official.

Calls to the congressman’s cellphone and to his press secretary went unanswered on Monday. But Mr. Amash politely parried his Republican critics on Twitter, writing that those who questioned his logic on impeachment were “resting their argument on several falsehoods.”

He has weathered controversies before — so often, in fact, that he has mainly used his Facebook page to defend positions and statements that have rankled, roused and puzzled.

There have been plenty. He dissented from Michigan’s congressional delegation in opposing federal aid to address the drinking water crisis in Flint. He came out against Mr. Trump’s increases in military spending and voiced opposition to House Republicans when they passed a symbolic resolution praising immigration enforcement officials, arguing that doing so would signify that all agents, regardless of their individual behavior, “were above reproach.”

But this fight is different. Mr. Amash, who serves in a safe Republican district in the Grand Rapids area, has gone from a marginal gadfly to an insurgent leader in the eyes of Mr. Trump and his supporters. On Monday, State Representative Jim Lower announced that he would oppose the five-term incumbent in 2020, the first of at least two, and possibly more, Trump-friendly Republicans who are considering challenging him in a primary next year.

“Justin has no fear,” said John Sellek, a veteran Michigan political operative who ran Mr. Romney’s campaign operation in the state when he was the Republican presidential candidate in 2012. “He’s been unafraid to be Mr. No on a lot of things, so generally he has been isolated and without a major accomplishment. To his credit, he’s also been unafraid to do repeated, relentless town halls — so he is both alone and out front at the same time. That puts you on an island, which is not a good place to be in a primary.”

Even if Mr. Trump actively opposes him, as he did successfully last year against another critic, former Representative Mark Sanford of South Carolina, Mr. Amash still commands high name recognition in his district, has a strong fund-raising base and could survive if the pro-Trump vote is split between two or more challengers, according to Mr. Sellek.