WASHINGTON, Oct 11 (Reuters) - Republicans in the U.S. House of Representatives met on Wednesday to choose between two candidates - Steve Scalise and Jim Jordan - to lead their narrow majority a week after a small group of dissidents ousted Speaker Kevin McCarthy.

As lawmakers gathered for the closed-door vote, neither candidate appeared to hold a clear advantage. Scalise, who is No. 2 on the leadership ladder, has drawn the support of many veteran and establishment Republican lawmakers, while Jordan, an outspoken leader of the party’s right wing, had the backing of many conservatives.

McCarthy could be in the mix as well, as he has not discouraged talk of a comeback, as could Patrick McHenry, the acting speaker.

The secret-ballot vote is the start of what could be a long and messy process to install a new speaker after a small faction of far-right Republicans deposed McCarthy last week and threw the chamber into chaos.

Before lawmakers start voting on a speaker, they are expected to decide on what threshold is needed to win: a simple majority of Republicans, or an absolute total of 217 votes, enough to ensure victory in the full House.

Representative Tom Cole said the higher threshold could allow a handful of holdouts to create gridlock, as they have repeatedly done this year. “It’s just overly complicated and we ought to just pick a winner,” he said.

Republicans, who control the House by a narrow 221-212 majority, say they need to quickly resolve a leadership vacuum that has prevented the House from addressing the war in Israel, approving more aid to Ukraine and passing spending bills before current funding runs out on Nov. 17.

“It’s really, really important that this Congress get back to work,” Scalise said.

Scalise and Jordan told Republicans at a closed-door forum on Tuesday night that they would each back the candidate chosen as nominee, an agreement that could help expedite matters.

VOTING COULD TAKE TIME

But some predict they will not be able to resolve their differences and unite behind a candidate quickly.

“My unfortunate estimation is that it will take several rounds and maybe even days of voting,” Republican Representative Ben Cline said in an interview.

It took only eight Republicans to oust McCarthy last week, a fact that could make leading the caucus a challenge for any new speaker.

Representative Ken Buck, one of the eight, said a “significant number” of Republicans could decline to vote for a candidate in Wednesday’s first ballot.

Buck said Jordan and Scalise provided unsatisfactory answers on the question of reining in spending on Tuesday night. He predicted that more candidates could join the race.

While McCarthy was the first speaker in U.S. history to be removed in a formal vote, the last two Republicans to hold the job wound up leaving under pressure from party hardliners.

Americans have little confidence in Congress’ ability to overcome its partisan differences - and the Republican infighting that led to McCarthy’s historic ouster on Oct. 3. Some 64% of respondents to a Reuters/Ipsos poll last week said did not believe Washington politicians could put aside partisan disagreements for the good of the nation.

Scalise and Jordan have both racked up several dozen endorsements, but neither has a clear path to success.

Difficult decisions could come if neither candidate wins a clear majority. Some moderates, for example, have warned that Jordan becoming speaker would give Democrats plenty of ammunition for next year’s congressional elections.

Others say they could be flexible if their preferred candidate doesn’t appear to be winning.

“I think Jim Jordan will end up getting it, and if not, Scalise would be fine,” said Representative Ralph Norman, who supports Jordan.