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

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

Former President Donald Trump, arriving to court for the third day of his civil fraud trial, commented on the speaker's race -- specifically, the calls from some hard-line conservatives such as Marjorie Taylor Greene for him to serve in the role.

"I'll do whatever it is to help. But my focus, my total focus is being president," he told reporters.

It's not the first time we've heard Trump's name floated for the position. Back in January, amid McCarthy's fraught battle for the gavel, Gaetz actually cast a ballot for Trump during one of the 15 rounds of voting.

It would technically be possible because the Constitution doesn't specify that the person be a current member or member-elect, but it's not likely.

Trump didn't say who he would like to see succeed McCarthy but said, "We have some great people in the Republican Party that could do a great job as speaker."

-ABC's Lalee Ibssa, Soorin Kim and Kendall Ross

Rep. Patrick McHenry, the new speaker pro tempore, is currently occupying the speaker of the House's office in the Capitol. Notably, the sign still reads "Speaker Of The House Kevin McCarthy."

-ABC's Arthur Jones