Amid House speaker vacancy, many in GOP want to do away with motion to vacate

House Majority Leader Steve Scalise has officially entered the race to replace McCarthy.

The Louisiana Republican, in a lengthy letter to his colleagues on Wednesday, made a pitch for unity as he touted his work as the No. 2 House Republican.

"You know my leadership style I've displayed as your Majority Leader and Whip," he wrote. "I have a proven track record of bringing together the diverse array of viewpoints within our Conference to build consensus where others thought it impossible."

"Our strength as a Conference comes from our unity, and we have seen when we unite as a Conference, we can deliver wins for the American people," he wrote. "Now we need to take those unified positions and work to extract conservative wins from the Democrat Senate and White House by leveraging upcoming deadlines. While we need to be realistic about what can be achieved, if we stay united, we can preserve leverage for the House to secure tangible wins in our impending policy fights."

Rep. Jim Jordan has sent a letter to colleagues announcing his speakership bid.

"We are at a critical crossroad in our nation's history," he wrote. "Now is the time for our Republican conference to come together to keep our promises to Americans."

Senate Republican leader Mitch McConnell said he is keenly aware of the thankless work it takes to be a Congressional leader as he praised McCarthy in a floor speech.

“I’ve said before, in reference to my own position, that being the leader of your party in the Senate is much like being the groundskeeper at a cemetery. Everybody’s under you, but no one’s listening," McConnell said, adding: “Of course, I doubt that Kevin McCarthy has ever seen himself as above anyone else."

McConnell praised McCarthy's willingness to dive "head first" into worthwhile fights, calling him a trusted and honest partner in leading the GOP caucus.

“He didn’t hesitate to get his hands dirty. When circumstances were tough, he drew on his faith, his family and his belief in American exceptionalism," McConnell said.

“And I’m not sure anyone could have predicted just how much these qualities would come in handy over the past nine months," he said.

-ABC's Mariam Khan

Rep. Jim Jordan, R-Ohio, told reporters Wednesday morning that he is running for speaker of the House -- the first member to publicly throw their hat in the ring.

Jordan, a top Trump ally and chairman of the House Judiciary Committee, has ruled out running for speaker in the past.

Jordan said Wednesday morning that the messages and phone calls of support he has received so far "seems strong."

"I think the key is to unite the conference," Jordan said. "I think I can."

In addition to Jordan, House Majority Leader Steve Scalise has begun making calls to gauge support as has Oklahoma Rep. Kevin Hern.

-ABC News' Katherine Faulders and Arthur Jones