Representative Matt Gaetz pressed forward on Monday evening to remove Speaker Kevin McCarthy from his post, setting the stage for a dramatic showdown this week between Mr. McCarthy and his conservative critics.

Mr. Gaetz, a Republican from Florida, made what is known as a motion to vacate. Any single lawmaker can make such a motion, and the House must hold a simple-majority vote on whether to remove Mr. McCarthy from the speakership within two legislative days. Mr. McCarthy agreed to allow any member to force such votes during a protracted floor fight in January as a concession to right-wing holdouts in exchange for the speakership.

The motion is privileged, meaning it takes priority in the House’s legislative agenda and requires action within two days. The House of Representatives convenes at 10 a.m. on Tuesday, and legislative business begins at noon, the earliest that the motion could be acted upon.

Mr. McCarthy can use several strategies to avoid or at least delay the vote. He could hold a majority vote to table the resolution, effectively killing it, and he could also refer it to a committee of his allies. He engineered a similar move in June that sidestepped an attempt to quickly impeach President Biden.

The Republicans’ slim majority means Mr. McCarthy has little chance of surviving without at least some help from Democrats. They could vote against Mr. McCarthy’s removal, vote “present” — neither yes or no — or skip the process entirely to lower the threshold of votes he needs to survive. As of Monday, House Democrats had not signaled their intentions, and it was Mr. McCarthy’s reliance on their support to avoid a government shutdown over the weekend that prompted Mr. Gaetz’s motion in the first place.

It is extremely rare for members of the minority to vote for the opposing party’s candidate for speaker. Democrats voted in unison for their leader, Hakeem Jeffries of New York, in each of the 15 rounds of the speakership fight in January. And Mr. McCarthy’s efforts to appease far-right members within his party since then, including launching an impeachment inquiry into Mr. Biden last month, have further frustrated Democrats.

Mr. Gaetz would need only a handful of Republicans to join his effort to remove Mr. McCarthy if Democrats remain unified against him. The more Republicans side against the speaker, the more votes Mr. McCarthy will need to win from Democrats if he is to remain in his post.

And even if Mr. Gaetz’s first attempt fails, he has indicated that he could keep trying until he has enough votes. His move on Monday was the third time in the 234-year history of the House that a speaker has faced a motion to vacate. Most recently, in 2015, Representative Mark Meadows of North Carolina filed a motion against Speaker John A. Boehner, who resigned from Congress before the House voted.