A small group of Republican strategists opposed to President Trump, branding themselves Defending Democracy Together, quietly conducted polling and focus groups last fall to gauge whether the president was vulnerable to a primary challenge in 2020. Assembling a presentation for sympathetic political donors, they listed points of weakness for Mr. Trump such as “tweeting/temperament” and “criminality/corruption.”

The group concluded that Mr. Trump’s scandals were not yet badly damaging him with Republican-leaning voters: “Even relatively high information voters aren’t paying particularly close attention to day-to-day scandals,” the presentation stated. But it added that there was “room to educate voters” on the subject.

Michael D. Cohen, Mr. Trump’s former lawyer, may have begun that education on Wednesday.

With Mr. Cohen’s appearance before a House committee, the public airing of ethical transgressions by Mr. Trump reached a new phase, one that may be harder to ignore for friends and foes alike. The spectacle of Mr. Trump’s onetime enforcer denouncing him in televised proceedings, detailing a catalog of allegations of cruelty and crimes, signaled the pressure the president’s already strained coalition could feel in the coming months as Congress scrutinizes him, and as the special counsel Robert S. Mueller III completes his investigation.

Republicans still find it difficult to imagine that Mr. Trump’s electoral base would ever desert him, though they acknowledge that bond may soon be tested as never before. Mr. Trump’s core supporters — numbering about two in five American voters, polls suggest — have stayed with him through revelations of financial and sexual impropriety, painful electoral setbacks and the longest government shutdown in history.