Brendan Buck, a past adviser to former Speaker Paul D. Ryan, said a debate where everyone agrees that Mr. Trump deserves to be impeached is a snooze and a wasted opportunity.

“Other than Biden having his opportunity to say his piece, they’re generally better off leaving this debate to Nancy Pelosi,” Mr. Buck said. The impeachment probe, he said, “isn’t terribly tangible to people’s lives.”

Nor is it how most Americans would like to see Mr. Trump leave office. A recent NPR/PBS NewsHour/Marist poll found that 58 percent of Americans think Mr. Trump’s fate should be decided by voters next November, compared to 37 percent who think it should be decided by the impeachment process. (Even so, 52 percent of respondents in that poll approved of the decision to begin the impeachment inquiry.)

The focus on impeachment may make it difficult for lower-polling candidates like Beto O’Rourke, the former Texas congressman, or Senator Cory Booker of New Jersey to break through. But Democrats said that over all, the inquiry would be a huge gift to whoever emerged as the party’s nominee.

“It’s creating a permanent black cloud that will ultimately help the Democratic nominee,” Mr. Fallon said, pointing to the earned media coverage of impeachment as a way for Democrats to close the messaging gap with the Trump campaign, which is vastly outspending them online.

“It’s defining him in a way none of the individual campaigns could do during a primary,” Mr. Fallon said. “They should all be thanking their lucky stars.”