Despite the efforts of pro-impeachment activist groups to transform August into a Tea Party-style series of grass-roots revolts that might force Democrats of all stripes to throw their support behind impeachment, the groundswell has yet to reach this politically crucial group of lawmakers in Republican-leaning districts. Instead, they are staying cautious and, in some cases, even trying to avoid mentioning the word, and many of their constituents — even impeachment supporters — appear willing, at least for now, to tolerate that reluctance.

In more than two dozen interviews in districts like these in three states over the past week, some voters said they wished their representative in Congress would hurry up and endorse an impeachment inquiry in order to send an unmistakable signal that Mr. Trump’s actions were illegal and unacceptable. But most were either strongly opposed or said they understood the reluctance to set the process in motion, given the degree to which it could divide the country, the likelihood of failure given Republican control of the Senate and the political stakes for their representatives if they backed it.

“The main issue is letting it play out in the 2020 election,” said Blaise Molitoris, Ms. Onelio’s sign-toting husband, who called Ms. Slotkin’s circumspection“fair” and said he understood her stance despite his own eagerness to see Mr. Trump impeached. “It’s not good for the country — just the divisiveness — but leaving it as is and not holding the president accountable for his actions just can’t stand in my book.”