Now the progressives who have long clamored for Mr. Trump’s removal and the moderates who stubbornly resisted it have come together around the idea that it is time to pursue an impeachment inquiry. The rare bit of unity has given leverage to House Speaker Nancy Pelosi, who has privately advised some of the freshmen about the most effective way to make their voices heard, as she undertakes a process that could bring down a president.

And balancing their competing interests as the House moves ahead could prove a steep challenge.

Top Democrats say it is no accident that Ms. Pelosi’s head-spinning turn from opposing an impeachment inquiry to calling for one came less than 24 hours after seven first-term moderates, including military veterans and two former C.I.A. officers, embraced the idea in the opinion pages of The Washington Post on Monday night. Other moderate freshmen followed with their own carefully drafted statements. Most had strongly resisted impeachment and some have tough re-election races.

“It caused other colleagues to change their minds and it signaled the gravity of the moment,” said Representative David Cicilline, of Rhode Island, a member of the Democratic leadership. “It wasn’t a coincidence that all these events happened together. As they began to call for it, it created, really, a dam breaking in our caucus.”

That has created a new atmosphere in the Capitol, where the moderates have spent months ducking reporter’s impeachment questions, often refusing to mention the word. Eclipsed in the media by liberals like Ms. Tlaib and Representative Alexandria Ocasio-Cortez of New York, they are now taking their turn in the spotlight, forthright about their views on and off camera.

“I support the inquiry, and I think the transcript that came out, it’s plain for anyone to see, it shows the president of the United States, both explicitly and implicitly asking a foreign leader to dig up dirt on a political opponent,” declared Representative Elissa Slotkin of Michigan, a former C.I.A. analyst and one of the authors of the op-ed. “That can’t be O.K.”