Washington (CNN) Conservative momentum to oust John Boehner from House leadership during Tuesday's election for speaker continued to build through the weekend, with two alternatives emerging and a national conservative group joining the effort.

On Monday, Virginia Rep.-elect Dave Brat became the latest to confirm his intention to vote against Boehner for speaker. On Sunday night, Arizona Rep. Paul Gosar and Iowa Rep. Steve King also came out opposed to Boehner.

In an op-ed published on Breitbart.com, King outlined a litany of complaints with the Speaker, arguing Boehner hasn't done enough to oppose President Barack Obama's signature health care law or the President's executive action on immigration and pointing to passage of the recent government funding bill, which tackled neither, as evidence.

Leadership aides, however, remain confident that Boehner will hold onto his position as the top Republican in the House. Conservatives need to gather nearly 30 lawmakers opposed to him to force a second round of voting in the race.

But the developing coup attempt is the latest reminder for the Ohio Republican that conservatives remain a troublesome and unpredictable force in his caucus that can cause public embarrassment if not out-and-out regime change.

"We need a Speaker who will help us all keep our oath, including his own, to the Constitution, not one who has consistently blocked our efforts to keep ours. I will vote for an alternative candidate for Speaker," King wrote

Those frustrations are shared by many of his fellow conservatives, and the passage of the cromnibus last month pushed already simmering tensions with Boehner to a boiling point.

And it threatens to start things off on precisely the wrong foot for Republicans as they take full control of Congress and seek to prove to Americans they're the party that can govern in time for 2016.

There are at least 10 lawmakers who have publicly said they'll oppose Boehner or vote "present" in the election for speaker.

GOP Reps. Ted Yoho of Florida and Louie Gohmert of Texas both offered themselves up as alternatives to Boehner this weekend, after two prominent conservatives in the House — Rep. Jim Bridenstine of Oklahoma and Thomas Massie of Kentucky — came out publicly opposed to him

North Carolina Rep. Walter Jones, an early organizer of the effort to unseat Boehner, told a local North Carolina paper that he plans to support Rep. Daniel Webster of Florida, whose name will also be offered as an alternative to Boehner on Tuesday.

"I want us to have a leader who is willing to stand up for conservative, religious principles I believe in. It is to make a statement and it's based on many months of consideration," Jones said.

National conservative group FreedomWorks has launched a national campaign in support of the effort, urging its members to call their lawmaker and tell them to vote against the Ohio Republican as speaker. And Bridenstine launched a short-lived website pitching Gohmert as speaker that included endorsements from both himself and Massie for the Texas Republican, which was soon after wiped of its content.

Still, none of the lawmakers who have offered themselves as potential alternatives are favorites of the far-right. Other prominent conservatives, including Fox News host Sean Hannity, have offered Rep. Trey Gowdy up for the job, but Gowdy has declined.

A coup attempt orchestrated by many of the same lawmakers two years ago fell short of the votes needed to force a second ballot, with only a dozen conservatives voting against Boehner.

And since then, many of those have expressed a change of heart, coming out in support of the Ohio Republican as Speaker — including prominent conservative Reps. Mick Mulvaney, Tim Huelskamp and Raul Labrador.

But conservatives say they're confident now that alternative options have stepped forward, they can corral the needed votes to at least force the election to a second ballot, where they hope Boehner will drop out of the race.

They also note that many members of the freshman class promised to vote against Boehner on the campaign trail — including Dave Brat, the Republican who ousted former Majority Leader Eric Cantor in a primary -- and are looking to them to round out their numbers. On Monday morning, Brat stood by that promise , also in an op-ed on Breitbart.

It's unclear what efforts leadership has undertaken to whip support for the speaker. Colorado Rep.-elect Ken Buck, the GOP freshman class president, said he hasn't heard from the speaker — but he has heard from Boehner's opponents.

"I have not talked to anybody in the Speaker's office. I have not talked to the Speaker. I have not heard that he is reaching out to anybody in the freshman class," Buck told CNN in an interview Monday. "On the other end, I have received some calls."

Daniel Horowitz, a conservative strategist and editor of ConservativeReview.com, said that the situation is "very fluid" but expressed cautious optimism.

"This is a much more robust effort than any of us ever hoped," he said.

He noted, however, that "things could still fall apart" in the final day before the election, and that he expects Boehner and his allies are applying heavy pressure on the incoming freshmen to make sure they fall in line.

Following the last coup attempt, a handful of the members who voted against Boehner were removed from their positions on plum House committees.

This time around, conservatives say they're not worried about punishment. Yoho said on Monday during an interview on Fox News that "I fear no man."

"There should not be any retribution. We're doing what my voters want me to do," he said.

But he promised to support whomever eventually wins the election for speaker — at least for the next session.

"I'll go up to 'em, I'll thank 'em and I'll tell 'em, you're the speaker for the next two years, and I look forward to working with you to solve America's problems," he said.

PUBLICLY OPPOSED TO BOEHNER (10)

Rep. Louie Gohmert (R-Texas)*

Rep. Ted Yoho (R-Fla.)*

Rep. Jim Bridenstine (R-Okla.)*

Rep. Thomas Massie (R-Ky.)*

Rep. Walter Jones (R-N.C.)* — Has been whipping votes against Boehner and says he'll back Florida Rep. Daniel Webster instead

Rep. Steve King (R-Iowa)

Rep. Paul Gosar (R-Ariz.)

Rep. Marlin Stutzman (R-Ind.) — Bridenstine says he's been told Stutzman will vote against Boehner

Rep.-elect Dave Brat

Rep.-elect Gary Palmer (R-Ala.) — Expressed regret for his opposition to Boehner on the campaign trail, but said he was committed to at least voting "present"

POTENTIAL NO VOTES:

Rep. Daniel Webster (R-Fla.)

Rep. Justin Amash (R-Mich.)*

Rep. Steve Pearce (R-N.M.)*

ELECTED REPUBLICANS WHO'VE OPPOSED BOEHNER WHILE CAMPAIGNING:

Rep.-elect Jody Hice (R-Ga.)

Rep.-elect Barry Loudermilk (R-Ga.)

Rep.-elect John Ratcliffe (R-Texas)

OPPOSED BOEHNER IN 2013 BUT CHANGED MIND SINCE

Rep. Tim Huelskamp (R-Kan.)

Rep. Raul Labrador (R-Idaho)

Rep. Mick Mulvaney (R-S.C.)

*Voted against Boehner for speaker in 2013