Then there is the most prominent Republican to have started invoking the specter of a Democratic-controlled House impeaching Mr. Trump: the president himself. In just the last month, he has used three separate speeches to warn that Representative Maxine Waters, a veteran California Democrat he has casually insulted as a “low-I.Q. individual,” aims to impeach him.
Advisers to the president say they have made clear to him that Republican control of the House is tenuous, and some have encouraged him to more aggressively lay out the stakes for the midterm elections, including who exactly would be in charge of key committees should Democrats retake the chamber.
“Everybody has told him that,” Corey Lewandowski, Mr. Trump’s former campaign manager, said about the prospect of a Democratic takeover of the House. “The threat of impeachment is something that unifies everybody in the party, even if you’re not a big Trump supporter.”
Democrats are divided on how to respond to the charge. Many top officials in the capital fear it is a political trap that would distract from their core message and possibly even boomerang back to harm them in November. But other more progressive figures see impeachment as a rallying cry of their own to galvanize the left’s anti-Trump base.
“I’ve been urging members to refrain from discussing impeachment,” said Representative Adam Schiff of California, the ranking Democrat on the House Intelligence Committee, adding: “I think we should let these investigations conclude and see what evidence is found.”
The mere thought of impeachment could energize Trump supporters who may otherwise be disinclined to vote in the midterm elections without him on the ballot, supporters of the strategy say.
“I can’t even imagine the Democrats would go there,” said Mark Lundberg, the former chairman of the Sioux County Republican committee in Iowa. “Impeachment for what? For being rude to them? That would be so outrageous.”
And to those voters in the political center who may be uneasy with, or simply exhausted by, his tumultuous administration, the possibility of an even more chaotic 2019 in Washington is unappealing.
Representative Patrick McHenry of North Carolina, a member of the House Republican leadership, predicted that the possibility of impeachment would divide the hard left from the broader political mainstream.
“It separates their base from reasonable, rational people that decide elections,” said Mr. McHenry, noting that this bloc of the electorate does not “want to put people in power that are going to create complete chaos and in essence shut down any potential legislative progress.”
But the mere fact that Republicans are talking by early spring about running on an impeachment threat reveals the depth of their challenge going into this fall’s election. The first midterm campaign of a new administration is typically difficult for the president’s party. But the tempestuous Mr. Trump has compounded the Republicans’ difficulties by generating an unending stream of made-for-TV controversies that overshadow their policy achievements and the health of the economy.
There are voices in the Republican Party who believe that it is too soon to sound the alarm, and that doing so will come off as overly panicked. Indeed, what is striking about the politics of impeachment is that both parties are divided over how to navigate the issue in the midterm campaign.
Polls show most voters are not supportive of impeachment at the moment, but if Mr. Trump were to fire the White House special counsel, Robert S. Mueller III, the country would become about evenly divided on the question.
In January, 66 House Democrats, over a third of the caucus, voted to begin impeachment proceedings. That was eight more than the total number who voted for a similar measure in the House a month earlier.
“I think he’s committed impeachable offenses,” said Representative Steve Cohen of Tennessee, adding that waiting for the special counsel is risky because Mr. Mueller’s inquiry may never “see the light of day.”
The Democratic leadership, though, has sought to tamp down these impulses. They believe Republicans are setting a trap and are irritated that the billionaire donor Tom Steyer, who recently said he wants to host a series of primary debates this year, is trumpeting the issue. These Democrats argue that the party needs to focus on a substantive agenda and assure voters that they will exercise sober and reasonable oversight of Mr. Trump.
On Thursday, the House Democratic campaign organization released a memo based on an internal poll that urged candidates to “express a willingness to work with the president when his agenda might help the district.”
“If impeachment becomes a political tool instead of the end result of a credible investigation, then you are as guilty as Trump, in some ways, of taking a hammer blow to institutions,” said David Axelrod, former President Barack Obama’s onetime chief strategist, adding that it would also create risks in swing districts. “To say I’m for impeachment come hell or high water is to promise chaos.”
And Democratic lawmakers say they are wise to the bait that Mr. Trump is placing before them when he invokes Ms. Waters, an outspoken black woman whose jeremiads against the president conservative media outlets delight in amplifying.
“They’re trying to encourage us to be more out front on impeachment so then they can use that to rev up their base and say, ‘That’s all the Democrats care about,’” said Representative Dina Titus of Nevada, a political-science professor by training.
To some Republican strategists, waving the bloody shirt of impeachment is unwise — at least this early in the election season.
“Republicans should leave that insanity to the left,” said Mike Shields, who worked for former Speaker Newt Gingrich during the Clinton impeachment wars of the 1990s. “We should be talking about the soaring economy, record low unemployment, 90 percent of workers getting tax cuts, defeating ISIS, and peace through strength on the Korean Peninsula.”
But other veteran party officials say what they are doing now is precisely what Democrats should have done to rouse their own voters, and protect their House majority, in the elections leading up to former President Bill Clinton’s impeachment in 1998.
“If the Democrats had been smart in ’94 and ’96, this would have been their message,” said Ralph Reed, a longtime Republican strategist, noting that buildup of what he called a “Clinton investigatory complex” made it clear Republicans intended to eventually impeach Mr. Clinton.
The group Mr. Reed runs, the Faith & Freedom Coalition, recently sent out a fund-raising solicitation seeking small contributions that warned about what it called the “Impeachment Election!” “Will you do your part to help stop this coup attempt by the radical anti-Christian left and the media against our duly elected president?” the letter read, with “stop” and “coup” in all capitals.
Other groups, some even more marginal, have filled the mailboxes of grass-roots conservatives with similar high-decibel appeals.
But what is notable is how this fire-and-brimstone approach is making its way into the party’s mainstream.
Last week, America Rising, a Washington-area candidate-tracking and opposition-research firm that assists Republicans, sent out a fund-raising email that read, “Right now the only thing standing between the president and the Democrats’ underhanded impeachment attempts is the Republican majority in the House fighting to defend our president.”
Or as Representative Sean Duffy of Wisconsin, a Republican, put in last week in a talk radio interview: “Do you think that the far-left Resist movement base of the Democrat Party would accept anything other than impeachment?”