A Washington Post-ABC News poll released on Friday appeared to underscore Democrats’ dilemma. It found that roughly six in 10 Democrats supported beginning impeachment proceedings against Mr. Trump, most of them strongly. But almost nine in 10 Republicans and six in 10 independents, whom Democrats need to defeat Mr. Trump, opposed the idea.

Democratic leaders in the House have pledged a series of hearings intended to ferret out the details of Mr. Mueller’s investigation and air the testimony of key witnesses. Rather than jump to conclusions — and there are some liberal lawmakers arguing in favor of prompt impeachment — party leaders say they want to build a case on live television before the public and see where that leads.

“We are going to do our work, but we’re not going to do it haphazardly,” Representative James E. Clyburn of South Carolina, the No. 3 Democrat in the House, said Sunday on the ABC program “This Week.”

He added, “Timing is everything in this business, and it’s one thing to run out a route, down a route toward impeachment; it’s something else to lay a foundation, gather the facts, educate the American people so that we can see exactly what needs to be done and when we should do it.”

For now, at least, the lack of pressure in districts that helped deliver Democrats their majority and united Republican support for Mr. Trump could help shape the road forward. Impeachment, Speaker Nancy Pelosi said last week at a Time magazine event, is “one of the most divisive paths we could go down in our country, but if the path of fact-finding takes us there, we have no choice.”

It is not that Democratic voters are counseling kindness. In Flava’s in Miami, the iconic restaurant’s owner, Wilbur Bell, agonized to Ms. Mucarsel-Powell that House Democrats were standing idly by while the president “disrespects their summons and subpoenas.”