Freedom Caucus members haven’t offered their own candidate for speaker, and it isn’t clear that they will back one of the current contenders, who along with Mr. McCarthy include Reps. Jason Chaffetz (R., Utah) and Daniel Webster (R., Fla.). All three accepted an invitation to address the Freedom Caucus and three other conservative groups on Tuesday evening in a candidates’ forum.

But the caucus members do have enough votes to prevent Republicans from coalescing around a new speaker, threatening to disrupt the succession process. The House GOP is expected to meet Thursday to choose its nominee to succeed Mr. Boehner, probably Mr. McCarthy. But the next step in the process may not unfold as smoothly as usual, in which the majority party rallies behind its choice in a House floor vote for speaker…

For the Freedom Caucus to take a formal position in the speaker race and endorse a particular candidate, under its own rules, 80% of its members would have to agree. So far, it appears unlikely Mr. McCarthy could reach that level of support. Some members say they are getting calls from constituents urging a vote against Mr. McCarthy, and others express more favorable views about Mr. Webster.

“If 80% of HFC support McCarthy, then the group probably should be disbanded,” Rep. Justin Amash (R., Mich.) tweeted this week. “I’m not worried about that happening.”