Rep. Steve Scalise and Rep. Jim Jordan.
CNN  — 

House Majority Leader Steve Scalise and Rep. Jim Jordan both jumped into the race Wednesday to become the next House speaker, setting up a fight to replace Kevin McCarthy after his historic ouster.

House Republicans are even more bitterly divided in the aftermath of House Speaker Kevin McCarthy’s ouster and his decision not to run again. It remains to be seen whether the conference can coalesce around a viable successor to the California Republican.

The stakes are extremely high as Congress faces down a looming shutdown deadline in mid-November. The House is essentially paralyzed while it lacks a speaker.

Republicans are slated to hear from speaker candidates at a forum next Tuesday, setting up the next possible House-wide speaker vote next Wednesday, October 11.

As Scalise and Jordan enter the race, Oklahoma Rep. Kevin Hern, who chairs a conservative group known as the Republican Study Committee, said Wednesday he is still looking at running for speaker but has not made a decision yet.

He said he wants the conference to “move forward” and they need to “be pointing our guns outward not at each other.”

House Republicans face leadership shakeup