The 20 hard-right Republicans who have repeatedly derailed Representative Kevin McCarthy’s ambitions to become speaker includes a core group of rabble rousers who disdain him and will never support him, a larger set of outspoken conservatives who are agitating for changes in how the House functions, and newly elected lawmakers who are choosing a leader for the first time.
Mr. McCarthy’s monthslong effort to appease them — capped off by a frenzied few days of humiliating defeats on the House floor this week — has so far fallen flat, raising questions about his vote-counting abilities, and about whether they can ever be placated.
Some have strongly suggested that they can, and the California Republican has agreed to many of their demands, including moves that would weaken the speakership considerably and make it exceedingly difficult to pass the most basic legislation, including bills needed to keep the government open and to avoid a default on the nation’s debt.
But the group is still aligned against him, and it remained unclear whether they could be won over — and what it would take.
Here is a closer look at the House Republicans standing in the way of Mr. McCarthy’s election as speaker:
The “Never McCarthy” Camp: 3.
Representatives Matt Gaetz of Florida and Lauren Boebert of Colorado have remained the most outspoken opponents of Mr. McCarthy.
F.A.Q.: The Speakership Deadlock in the House
A historic impasse. Representative Kevin McCarthy of California is fighting to become House speaker, but a group of hard-right Republicans is blocking his bid and paralyzing the start of the new Congress. Here’s what to know:
It appears particularly personal for Mr. Gaetz, who emerged from a closed-door meeting on Wednesday to declare the Republican leader “a desperate man” and pledge that he would “vote all night, all week, all month — and never for that person.” He voted for former President Donald J. Trump on Wednesday.
Ms. Boebert has also repeatedly gone on television to defend the stance against Mr. McCarthy, even as pressure has mounted from Mr. Trump and conservative allies outside of Congress. And she scoffed on Thursday at the notion Mr. McCarthy’s many concessions would be sufficient to deliver him the votes to become speaker.
“Not enough to make him speaker,” she told a reporter, adding, “bless his heart.”
Representative Bob Good of Virginia, a self-described “biblical conservative” and former administrator at Liberty University, also made it clear on Thursday that he would never be swayed to Mr. McCarthy’s side.
“You don’t ever have to ask me again if I’m a no,” he said. “I will never vote for Kevin McCarthy.”
The Negotiators: 5.
Some of the detractors have been involved in intense negotiations with Mr. McCarthy’s allies, seizing the opportunity to force changes to the House’s power structure and ensure that rank-and-file lawmakers hold more influence over the process. They have signaled that they would be willing to shift their support to Mr. McCarthy if he acceded to their demands.
That group includes Representative Chip Roy of Texas, the former chief of staff to Senator Ted Cruz, who has weaponized his procedural knowledge to force delays in House proceedings and call for an overhaul of the chamber rules. It also includes Dan Bishop of North Carolina and Representative Byron Donalds of Florida, a second-term Republican who emerged as a consensus pick for Mr. McCarthy’s foes on Wednesday. (Mr. Donalds has openly said he does not want the position, but since joined negotiations.)
Mr. Donalds, like Mr. Roy, pointed to a provision that would allow a single lawmaker to force a snap vote at any time to oust Mr. McCarthy from the speakership as a key priority.
Representative Scott Perry of Pennsylvania, the current Freedom Caucus chairman who was involved in efforts by Mr. Trump to remove the acting attorney general who stood by the results of the 2020 election, has also been involved in the talks. But on Thursday, he lashed out at Mr. McCarthy and his allies, accusing them of leaking details of their talks to reporters.
“A deal is NOT done,” he wrote on Twitter. “When confidences are betrayed and leaks are directed, it’s even more difficult to trust.”
He added: “I will not yield to the status quo.”
Representative Ralph Norman of South Carolina has also shown an openness to haggling. When asked if he would be open to voting for Mr. McCarthy after the new round of concessions, he replied: “The devil is in the details.”
The Unknowns: 12.
Several of the lawmakers who have declined to back Mr. McCarthy have not answered questions about what would be needed to convince them to drop their objections, or avoided a grilling from conservative media outlets.
Representative Matt Rosendale of Montana was among the returning lawmakers who continued to vote for someone other than Mr. McCarthy, along with Representatives Mary Miller of Illinois and Andy Harris of Maryland.
Some of the lawmakers have pushed for votes on specific bills, like legislation requiring term limits for lawmakers. The group has also demanded their own representatives to sit on the powerful Rules Committee, which controls what legislation receives votes and the terms for debate on the House floor.
And there are some reports that a few of the lawmakers are angling to lead specific committees, though some of Mr. McCarthy’s supporters have pointedly noted that such decisions are up to a separate group of Republican lawmakers, not just the speaker.