RENO, Nev. — Representative Mark Amodei was not prepared for the backlash from his fellow Republicans when he said Congress needed to “follow the facts” and look into whether President Trump should be impeached.

Newspapers declared he was breaking ranks. Conservative constituents branded him a traitor: “I’m Brutus, and Trump’s Julius Caesar,” he said. In short order, he was forced to explain himself to the Trump campaign’s political director, top House Republicans and the acting White House chief of staff. All had the same question: “What the heck are you doing?”

As evidence mounts that Mr. Trump engaged in an intensive effort to pressure the leader of Ukraine to investigate a political rival, Mr. Amodei is one of a growing number of Republicans who, while not explicitly endorsing the Democrats’ impeachment inquiry, are at least indicating an openness to it. None have said Mr. Trump should be impeached. But neither are they defending him.

It is a politically delicate but increasingly common approach among independent-minded lawmakers like Mr. Amodei, who are working to balance their fear of inviting Mr. Trump’s wrath — and that of the party base — with a deep anxiety that there is more to be revealed about the president, some of it potentially indefensible, and the knowledge that history will hold them accountable for their words and actions.