Originally Published: 03 JAN 23 16:30 ET

Updated: 03 JAN 23 18:54 ET

By Sonnet Swire, CNN

(CNN) -- Conservative hardliners nominated Rep. Jim Jordan of Ohio on Tuesday to be speaker of the House during the chamber's second and third votes amid the floor fight for House leadership.

Jordan, in an effort to show party unity, nominated GOP leader Kevin McCarthy in the second round of voting. Speaking on the House floor Tuesday, Jordan said the differences among Republican lawmakers "pale in comparison" to the differences between Republicans and Democrats.

"We need to rally around him," Jordan said of McCarthy.

Rep. Matt Gaetz of Florida nominated Jordan in the second round where he earned 19 votes. Republican Rep. Chip Roy of Texas, who already voted twice against McCarthy, nominated Jordan for speaker in the third round.

In that round, Jordan earned 20 votes when Rep. Byron Donalds of Florida, who had initially voted for McCarthy in the first two rounds, shifted his support to Jordan.

Jordan's nomination by other members marks a new layer of leadership drama as Republicans take control of the House. The first order of House business as the 118th Congress convenes is the selection of a new speaker, but McCarthy is being stonewalled by a group of conservative hardliners. Because the GOP holds only a narrow majority, those hardliners hold more influence in the conference and have already denied McCarthy the votes necessary to secure the gavel in initial rounds of balloting.

A majority of at least 218 votes is needed to be elected speaker. The tally for the first ballot in the speaker vote was 203 for McCarthy, 10 for Rep. Andy Biggs and six for Jordan -- with three Republicans voting for other candidates.

For McCarthy to reach 218, he can only afford to lose four GOP votes -- and his initial failure to do so marks the first time in a century that a party will have to take multiple ballots to elect the chamber leader.

The House voted to adjourn Tuesday evening after McCarthy suffered his third rebuke for speaker and the number of defections against him grew. He earned 202 votes on the third ballot.

Leaving the floor, Jordan told CNN there is "no" chance he will become speaker, adding he wants to be House Judiciary chairman. He said he would lobby his colleagues to back McCarthy once the chamber resumes Wednesday.

Jordan is a high-ranking conservative and a founding member of the conservative House Freedom Caucus, serving as its first chair from 2015 to 2017, and as its vice chair since 2017. He was the ranking member of the House Oversight Committee from 2019 to 2020. He vacated that position to become the ranking member of the House Judiciary Committee, where he is expected to become chairman in the newly GOP-held House.

Jordan is a close ally of former President Donald Trump. After Joe Biden won the 2020 presidential election and Trump refused to concede while making claims of election fraud, Jordan supported lawsuits to invalidate the election results and voted not to certify the Electoral College results.