With the election for speaker of the House less than a week away, Representative Kevin McCarthy is facing potentially critical opposition to his candidacy that could drag out the process and result in the new Congress starting with deadlock.

Mr. McCarthy was the assumed next speaker until a lackluster Republican performance in November cast his leadership into doubt. Unlike the conference leadership elections in November, he’ll need a majority of the House to vote him into the speakership in January.

With Republicans holding a nine-seat majority, Mr. McCarthy can only afford four dissenting votes from his conference if he’s to clinch the speakership.

As it stands, there are at least five Republicans standing in opposition to Mr. McCarthy — Congressmen Andy Biggs, Bob Good, Matt Gaetz, Matt Rosendale, and Ralph Norman. These representatives have stated that they won’t support Mr. McCarthy under any circumstances.

“Kevin McCarthy, when are you going to realize you don’t have the votes to be Speaker?” Mr. Gaetz said in a tweet. “Any sort of ‘chaos’ on that day would be caused by McCarthy’s denial, not by our principled stand.”

Mr. Biggs, who is Mr. McCarthy’s sole challenger as of now, has predicted other Republicans will break with Mr. McCarthy after the first round of voting if Mr. McCarthy comes up short of the required 218 votes.

The Republicans most likely to break with Mr. McCarthy are expected to be members of the Freedom Caucus on the right flank of the Republican conference.

These include the caucus’s chairman, Congressman Scott Perry, as well as Congressmen Chip Roy, Dan Bishop, Andrew Clyde, and Paul Gosar; Congresswoman Lauren Boebert; and Congressmen-elect Eli Crane and Andy Ogles.

During an appearance on “The Charlie Kirk Show,” Ms. Boebert said she and her allies want certain House rules changed in exchange for their support. “You cannot demand more responsibility without accountability,” she said. Ms. Boebert hasn’t clarified whether she will support Mr. McCarthy if he gives in to these demands, stating only that these are her demands of whomever is elected speaker.

The rule changes sought by Ms. Boebert and others, circulated in a letter from early December, include requiring that bills brought to the floor concern only one subject; a 72-hour reading period prior to votes on bills; and the restoration of the motion to vacate the chair, which would allow for the removal of the speaker.

In the letter, Mr. Perry wrote that “the House leadership of both parties has increasingly centralized decision-making power around fewer and fewer individuals — at the expense of deliberation and input by the body.”

The Freedom Caucus is, however, not unified in their opposition to Mr. McCarthy’s leadership. Ms. Greene has emphatically thrown her support behind Mr. McCarthy, creating friction between her and her frequent ally, Ms. Boebert.

After weeks of closed-door negotiations, it’s unclear exactly how many votes Mr. McCarthy will receive in the first round of voting on January 3, but the Republican conference leadership elections might serve as an estimate.

In the party elections, Mr. McCarthy received 188 votes in support of his leadership, and 31 representatives opposed him. Three members have been added to the conference since the vote because it was held before every House race had been decided.

If Mr. McCarthy comes up short next week, things are bound to get messy. The House clerk would, in that scenario, have to call additional votes until someone wins the 218 required to lead.

Lawmakers are also allowed to pause voting to take to the floor and cut deals with one another before returning for another round of voting. Among the options is changing the method of voting — such as to a secret ballot from a roll call vote.

Importantly, Mr. McCarthy, not being the speaker, will be subject to the ruling of the clerk, and effectively an equal with the other representatives. The outgoing clerk, Cheryl Johnson, will be in charge of making the rulings that a speaker normally would make while the House works through the election.

With the House being required to elect a speaker, and five Republicans saying they will oppose Mr. McCarthy’s speakership under any circumstances, a new candidate could arise during the election.

In 2015, the last Republican speaker, Paul Ryan, arose after a similar conflict between Mr. McCarthy and the Freedom Caucus. He was seen as a compromise candidate even though he was not running for the position prior to the conflict.

No such dark horse candidate has emerged yet in the upcoming speaker election. However, there has been no shortage of names floated as replacement for Mr. McCarthy.

The likes of President Trump, Vice President Pence, and Representative Liz Cheney have all been suggested by spectators as potential speakers, though they would be long-shot candidates. Although every speaker to date has been a member of the House, that is not a requirement under the Constitution.

Mr. Gaetz, one of the more stalwart anti-McCarthy Republicans, has publicly urged Congressman Jim Jordan to run for the position, though Mr. Jordan has not shown any public interest in pursuing the post.

A conservative commentator, Mike Crispi, has reported that an outgoing congressman, Lee Zeldin, is being floated as an alternative to Mr. McCarthy for the role of speaker; the Sun has been unable to independently verify this report.