The eight House Republicans who voted to remove Speaker Kevin McCarthy volunteered Friday to be punished in exchange for votes to elect Rep. Jim Jordan, R-Ohio, as the new speaker.

The gesture, however, quickly proved to be fruitless, as House Republicans voted behind closed doors against Jordan continuing his bid for the post. Hours earlier, Jordan fell short in a third vote for speaker.

The eight members sent a letter Friday to their Republican colleagues — some of whom are furious about the move to oust McCarthy — offering to be censured, suspended or removed from the GOP conference if it meant Jordan securing the necessary votes.

“The recent passage of the Motion to Vacate the Speaker has caused rancor, hurt feelings and acrimony in the House Republican Conference,” the letter reads. “While we stand by our actions, it is our goal to proceed forward with our colleagues, our teammates, our fellow Republicans in a manner that embraces reconciliation.

The eight members wrote that some have suggested House Republicans cannot move forward unless the McCarthy detractors are punished. 

“Therefore, if the holdouts who refuse to vote for Speaker-Designate Jordan would be willing to ‘vote with the team’ and elect him the 56th House Speaker, we are prepared to accept censure, suspension, or removal from the Conference to accomplish this objective,” the eight Republicans wrote. 

The letter was signed by Reps. Andy Biggs of Arizona, Ken Buck of Colorado, Tim Burchett of Tennessee, Eli Crane of Arizona, Matt Gaetz of Florida, Bob Good of Virginia, Nancy Mace of South Carolina and Matt Rosendale of Montana.

In the third ballot Friday, 194 Republicans voted for Jordan, and 25 voted for others. All 210 Democrats who cast ballots supported Minority Leader Hakeem Jeffries.

To be elected speaker, a candidate must receive a majority of votes from the full House.

Since receiving 200 votes in the first ballot Tuesday, Jordan has seen his support fall in each subsequent vote.

“Some of what we’ve heard by our colleagues [is] they don't want to support a vote for Jim Jordan because of the eight of us,” Mace told reporters Friday. “And so we sent a very sincere letter to our colleagues today to offer up punishment if they want to punish us, whatever it takes to get there.”

Added Gaetz, who led the effort to remove McCarthy: “If what these holdouts need is a pound of our flesh, we’re willing to give it to them in order see them elect Jim Jordan for speaker.”

Following the McCarthy vote, Reps. Don Bacon, R-Neb., and Mike Lawler, R-N.Y., both said they would like to see Gaetz removed from the conference. Neither Bacon nor Lawler voted for Jordan in the three ballots.

California GOP Rep. Mike Garcia appeared supportive of the idea.

"If they're willing to stand by that, regardless of who the nominee is, I think we should take them up on it," he said. "If that helps people feel better and helps the healing process."

McCarthy, for his part, called the group the "crazy eights led by Gaetz" and said that "the amount of damage that they have done to this party and to this country is insurmountable."

"We are in a very bad position as a party, one that has won the majority, one that America has entrusted us with, that a simple eight people have put us in this place," he added.