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

With Scalise in the race for speaker, Rep. Tom Emmer, the current GOP whip is running for majority leader and he has endorsed Scalise for speaker.

That would open up the whip’s spot. Potential contenders who are said to be interested for whip: Rep. Drew Ferguson of Georgia, who lost and ran last time, or Rep. Guy Reschenthaler of Pennsylvania, Emmer’s deputy. Reschenthaler confirmed on Wednesday he’s running for majority whip.

House GOP Conference Chairwoman Elise Stefanik is also calling colleagues and allies about potentially moving up the chain in leadership, a source familiar said.

Scalise and Jordan make pitch for unity

Scalise and Jordan both made a pitch for unity to House Republicans, an acknowledgment of the fractures within the conference following McCarthy’s exit.

“We must mend the deep wounds that exist within our conference and focus on our objectives so we can get back to work for the millions of people who are counting on us,” Scalise wrote in a letter to his colleagues asking for their support.

Scalise has experienced some serious health issues in recent years.

In August, he revealed that he had been diagnosed with multiple myeloma. In September, Scalise told reporters that in response to treatment, his cancer “has dropped dramatically.”

Scalise also survived a shooting in 2017 at a practice ahead of a charity baseball game that left him in critical condition.

In his letter to colleagues, Scalise referenced the shooting. “I firmly believe this conference is a family. When I was shot in 2017, it was members of this conference who saved my life on that field,” he said.

“I love this country, and I believe we were sent here to come together and solve the immense challenges we face. As I face new challenges, I feel even more strongly about that today.”

Jordan similarly called for House Republicans to “come together.”

“Now is the time for our Republican conference to come together to keep our promises to Americans,” Jordan wrote in a letter to House GOP colleagues obtained by CNN, adding, “No matter what we do, we must do it together as a conference.”

The Ohio Republican chairs the House Judiciary Committee, an important body for pursuing Republicans’ investigative priorities – including one of three committees behind the impeachment inquiry into President Joe Biden.

Jordan downplayed concerns on Wednesday that he may be too conservative for some of the more moderate members of the GOP.

“I think we are a conservative-center-right party. I think I’m the guy who can help unite that. My politics are entirely consistent with where conservatives and Republicans are across the country,” Jordan told CNN’s Manu Raju.

Tensions simmer after McCarthy’s ouster

The race for speaker abruptly got underway late Tuesday evening after McCarthy stunned Washington by announcing he would not run again after the House ousted him from the top leadership post in a historic vote that has left the House in uncharted territory.

As speaker, McCarthy presided over a narrow majority and had to confront criticism from hardline conservatives, who threw up roadblocks to the leadership agenda and protested legislation that passed with Democratic support. His ouster, led by GOP Rep. Matt Gaetz of Florida, came soon after he averted a government shutdown by passing a bipartisan stopgap funding bill.

Rep. Garret Graves, a McCarthy ally, criticized the move by Gaetz.

“Yesterday, effectively, someone threw a grenade right in the middle of the House floor,” Graves said. “There is a reason this has not been done in well over 100 years. This is not something that ever should have happened. I think it was done for narcissistic, for selfish reasons, for fundraising reasons. I don’t think it has anything to do with actually advancing conservative causes.”

With the House awaiting a new speaker, Graves also warned that there can only be limited action. “The House is frozen,” he said.

This story and headline have been updated with additional information.

CNN’s Manu Raju, Lauren Fox, Haley Talbot, Annie Grayer and Sam Fossum contributed to this report.