Kevin McCarthy looks to take the House speakership when the new Congress convenes this week, but he is still struggling to win over hard-liners who have been pushing for concessions that could weaken his authority. 

McCarthy, R-Calif., will have the critical backing of some Republicans from rural swing districts, who have vowed to oppose any other candidate for the post. The big question for the Jan. 3 House floor vote is whether McCarthy has done enough to win over enough of his right-wing critics.  

The new Congress convenes at noon Tuesday with Republicans holding 222 seats to 213 for the Democrats.

Democrats will retain control of the Senate, although Arizona Sen. Kyrsten Sinema announced in December she was switching her party affiliation from Democrat to independent. Democrats have 48 other seats, plus the backing of independents Angus King of Maine and Bernie Sanders of Vermont, who caucus with Democrats. 

Rep. Darrell Issa, R-Calif., expressed confidence Sunday that McCarthy would win the speakership, telling Fox News that the GOP opposition to McCarthy was dwindling.  

"You can’t make a decision on somebody with nobody, and quite frankly there is no alternative to Kevin. He clearly is our choice broadly, and he’s earned it," Issa said. 

But according to media reports, nine of McCarthy's right-wing critics issued a letter later Sunday saying he had not gone far enough in meeting their demands. A key demand has centered on the process for removing a speaker. 

In an earlier rebuff to McCarthy’s critics, 15 Republicans representing largely Democratic states signed a letter led by Rep. Mike Lawler, R-N.Y., Thursday calling for the party to unite behind McCarthy.

 “Let us be clear: we are not only supporting Kevin McCarthy for Speaker, but are not open to any so-called shadow ‘consensus candidate’ regardless of how many votes it takes to elect Speaker-designate McCarthy,” says the letter, a copy of which Lawler retweeted.

“There is no other conservative candidate that can garner the support of 218 Republicans for Speaker-period.”

The letter signers included Rep. David Valadao and Rep.-elect John Duarte, both farmers who won tough races in California’s Central Valley in November. Valadao is a member of the House Agriculture Appropriations Subcommittee, which writes the annual spending bill for USDA and FDA. Duarte hopes to join the House Ag Committee.

Also signing the letter was Nebraska Rep. Don Bacon, who won reelection in an Omaha-based district.

Lawler knocked off Democratic Rep. Sean Patrick Maloney, a member of the House Ag Committee who headed the Democratic Congressional Campaign Committee in the latest election cycle.

McCarthy's opponents were doubling down in their opposition to his leadership, however.

"Nobody has 218 votes, which is the magic number, and I don't believe we're going to see that until Jan. 3," Rep. Andy Biggs, R-Ariz., told Fox News on Thursday. "It may even take a few ballots to shake that out." 

Biggs said in a tweet, “I don’t see any scenario where I’d support Kevin McCarthy as House Speaker. McCarthy has a track record of cutting backdoor deals with Democrats.”

House GOP Whip Steve Scalise, who will become majority leader in the new Congress, has denied any interest in challenging McCarthy for the speakership and has expressed confidence McCarthy would get elected. 

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Heading into the holidays, McCarthy was meeting individually with his strongest critics, Scalise told Fox News. “Kevin is working to get there, and he’s going to get there,” Scalise said.  

In her final news conference, outgoing Speaker Nancy Pelosi, D-Calif., expressed confidence that Republicans could agree on a speaker, and she wasn’t concerned the House would be weakened by a protracted dispute.

“I do think the sooner the better because we have important work to do, whether we agree or disagree,” she said.

Despite the uncertainty over the speakership, Scalise announced plans on Friday for the House to move quickly on several bills that will highlight concerns with Biden administration policies and Democratic legislation.

The GOP bills, which would have little chance of passing the Senate, will include measures to rescind funding for additional Internal Revenue Service agents and block nonemergency drawdowns of the Strategic Petroleum Reserve "without a plan to increase energy production on federal lands."

The House is due to take up the IRS bill on Tuesday after the election for speaker. 

The new Senate will get off to a slower start than the House. The Senate convenes Tuesday, but its first work period will be the week of Jan. 23.

Several Senate veterans who didn't seek reelection will be missing on Tuesday, including Patrick Leahy of Vermont, who chaired the Appropriations, Judiciary and Agriculture committees during his eight terms. Other retiring members include Republicans Richard Shelby of Alabama and Roy Blunt of Missouri. 

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