Rep. Ted Yoho was the latest to publicly announce his decision not to support Boehner for his current position, making the news on his social media accounts Saturday night.
On Friday, Rep. Jim Bridenstine pointed to Boehner's moves in December to advance a measure favored by President Barack Obama to fund the government for the next 10 months.
"Speaker Boehner went too far when he teamed with Obama to advance this legislation. He relinquished the power of the purse, and with it he lost my vote," Bridenstine said in a statement.
Rep. Thomas Massie said Saturday he too would not support Boehner and said he opposed the way Boehner steered legislation the House floor, in some instances without a full 72 hours for lawmakers to read enormous bills.
"During my first two years as a congressman I discovered a significant source of the dysfunction. I watched the House Leadership," said Massie in a statement.
Massie and Bridenstine are unlikely to be the only Republican to vote against Boehner for speaker.
In a local radio interview first noted nationally by BuzzFeed
, Rep. Walter Jones (R-N.C.) said he'd been talking with 16 to 18 conservatives about identifying an alternative candidate for speaker and rallying around that person.
A freshman Alabama Republican, Gary Palmer, said in October that he'd told Boehner personally that he wouldn't be voting for him for speaker.
"I told him that if the first thing that I did when I got up there is violate my word to the voters, and break that trust, not only would I lose that confidence, but, immediately in the back of his head, he would be wondering at what point would I break my word to him," Palmer told The Birmingham News.
Dropping a few of his own party's votes in the speaker's race isn't new for Boehner. When the last Congress kicked off in 2013, there were nine Republicans -- including Bridenstine -- who voted against Boehner, and three others who didn't vote for a candidate for speaker. Most of them had complained that Boehner isn't enough of a hard-liner.
Indeed, in Bridenstine's note Friday, he said "our Constitution is under assault" because Republicans haven't fought strongly enough against Obama's moves to curb some deportations, restrict environmentally-harmful emissions, shift prisoners out of the Guantanamo Bay, Cuba detention facility and strike a deal to ease relations with Cuba. The wake of November's massive midterm victories for Republicans, Bridenstine said, was the best opportunity Republicans had to use their funding authority to rein Obama in.
"It seemed Democrats were melting down, Republicans were unified, and all we had to do was buy enough time to get our Republican reinforcements to Washington in January," he said.
The position that Boehner should be ousted has backing from Republican voters. Sixty percent said they'd pick someone new over Boehner for speaker, according to a survey
commissioned by The People's Poll, conducted by Caddell Associates and released this week.
Still, it's not clear that there are enough Republicans willing to reject Boehner to throw the vote for speaker into a second round.
The GOP holds 247 seats in the House, and Boehner will need a simple majority of 218 to be elected speaker. That means he can afford to lose 29 votes from Republicans -- assuming no Democrats support him.
If 30 or more Republicans do oppose Boehner, that would mean another round of voting, with conservatives hoping Boehner would drop out of the running and Boehner's allies likely heaping immense pressure on the hold-outs.