Rep. Jim Jordan (R-OH) has whittled down the number of opponents of his House speaker bid to less than a dozen, according to a GOP source familiar with his whip efforts.

The number shows that Jordan, the House Judiciary Committee's chairman, has made significant progress with members of his conference, 55 of whom said on Friday via a secret ballot that they would not vote for him on the House floor after he secured his party's internal nomination.

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A floor vote is scheduled for Tuesday, and Jordan has said he will go to the floor that day, even if he does not have the 217 votes locked up.

Building on the momentum, Jordan circulated a "Dear Colleague" letter on Monday morning, acknowledging worries about the shocking and discombobulated chain of events that led up to his nomination.

Those events included eight Republicans voting with Democrats to oust former Speaker Kevin McCarthy (R-CA) and House Majority Whip Steve Scalise (R-LA) clinching the internal nomination, only to be met with hard-liners who refused to support their new nominee.

"We've discussed frustrations about the treatment of Kevin McCarthy and Steve Scalise and the events of the past month," Jordan wrote. "In these conversations, we've also discussed your thoughts on how we can best move forward. And we must move forward."

Jordan saw a breakthrough Monday with some of his toughest critics, those who previously said they refused to vote for him on the floor.

House Armed Services Committee Chairman Mike Rogers (R-AL), who, unlike Jordan, supports funding Ukraine, announced he would vote for Jordan on the floor after having "two cordial, thoughtful, and productive conversations" with the Ohio Republican.

Rep. Ken Calvert (R-CA), a top appropriator in charge of defense funding, also revealed on Monday he would support Jordan, as did Rep. Ann Wagner (R-MO), a staunch Scalise ally who initially said she would not under any circumstances vote for Jordan.

Confusion remains rampant about just how many members are against Jordan and who exactly they are.

On a radio show, Rep. Chip Roy (R-TX), an ardent Jordan supporter, said that while he doesn't have an exact whip count, "his gut" tells him the number of holdouts is "somewhere south of 10." Two other GOP members said the same thing, with one saying they believe there are nine hard "no's," while the other said they believe it is closer to seven.

Regardless of who is correct, anything more than four members being against Jordan is enough to tank his chances.

This is why Jordan's team wants to take the vote to the floor, even if it has not locked up the 217 votes necessary to become speaker, in order to see who exactly is against Jordan, get them on the record, and then try hard to court their votes.

One senior appropriator, Rep. Steve Womack (R-AR), said on CNN that he doesn't think anybody in "America can get 217 right now out of the Republican conference. If that becomes apparent to everybody, then at some point in time, we're going to have to work across the aisle.”

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While he didn't share how he was going to vote on the floor come Tuesday, Womack did say that a lot of appropriators are concerned with the idea of Jordan becoming speaker.

"After all, two weeks ago, Mr. Jordan voted against the continuing resolution on the very day the funding was about to lapse," he said. "So he, in an essence, voted for a government shutdown, and I know that concerns a lot of appropriators."