Update (1515ET): Earlier Thursday, Jim Jordan said he wouldn't hold a third ballot for speaker, and would instead let interim speaker Patrick McHenry (R-NC) hold the gavel until January - with Rep. David Joyce (R-OH) drafting legislation to give McHenry the full powers that come with the job.

This rubbed many Republicans the wrong way, as McHenry is backed by Democrats.

"As I have made very clear over the last few days, we should never allow a Democrat-backed coalition government. Ever. The only coalition we should be looking to build is a Republican coalition uniting all of our conference," said Rep. Tom Emmer.

Steve Scalise, Jordan's previous opponent for speaker who pulled out, as well as Elise Stefanik (R-NY) arealso opposed to a Dem-friendly speakership going into January.