WASHINGTON — Rep.-elect Kevin McCarthy (R-Calif.) predicted Friday that he would become the next speaker of the House after more than a dozen GOP holdouts backed him once progress was made on a deal hashing out the rules of the 118th Congress.

After voting two more times — the 12th and 13th ballots of the marathon contest — the House voted to adjourn until 10 p.m. Friday, by which point McCarthy and his allies hoped to have locked up the 218 votes they were likely to need.

“We’ll come back tonight, and I believe at that time, we’ll have the votes to finish this once and for all,” McCarthy told reporters after the adjournment.

For the first time since balloting began Tuesday, McCarthy received the most votes from the members-elect by getting 213 on his 12th try — still three short of what was required due to absences on both sides of the House.

Democratic leader Hakeem Jeffries of New York received 211, with Rep-elect. David Trone of Maryland missing the vote to undergo shoulder surgery. (He later returned for the 13th ballot and received a standing ovation from fellow Dems when he voted.)

Two spoiler candidates, Republicans Jim Jordan of Ohio and Kevin Hern of Oklahoma, received four and three votes, respectively.

The mood on the GOP side of the House chamber, which had darkened considerably during an interminable set of five votes Thursday, brightened during the 12th ballot as 13 previous McCarthy opponents switched sides.

Each of the 13 — Dan Bishop of North Carolina, Josh Brecheen of Oklahoma, Mike Cloud of Texas, Andrew Clyde of Georgia, Byron Donalds of Florida, Paul Gosar of Arizona, Anna Paulina Luna of Florida, Mary Miller of Illinois, Ralph Norman of South Carolina, Andy Ogles of Tennessee, Scott Perry of Pennsylvania, Chip Roy of Texas and Keith Self of Texas — were cheered as they called McCarthy’s name at the clerk’s prompting.

Rep.-elect Victoria Spartz (R-Ind.), who voted for McCarthy on the first three ballots before switching to “present” Wednesday and Thursday, also switched back to the McCarthy camp on the 12th ballot.

“The American people have witnessed for the first time in this town in probably 100 years, if not more, a deliberative process – a legitimate, deliberative process – about the future of leadership in the people’s body,” Donalds told reporters after switching his vote. “That is monumental for all of the voters, whether they are Republicans or Democrats, to make sure that the people’s house is working for them.”

Of the remaining seven holdouts, Andy Biggs of Arizona, Matt Gaetz of Florida, Bob Good of Virginia and Andy Harris of Maryland supported Jordan — himself a McCarthy backer. Lauren Boebert of Colorado, Eli Crane of Arizona and Matt Rosendale of Montana voted for Hern — who also supported McCarthy.

On the 13th ballot, Harris switched to McCarthy, leaving six among the rebel ranks — all of whom backed Jordan, the presumptive House Judiciary Committee chairman, though none bothered to formally place his name in nomination.

On a conference call Friday morning, McCarthy confirmed that he was “willing” to change the House’s rules to allow a single member to make a so-called “motion to vacate,” which would trigger a vote on removing the speaker.

The Californian had previously held out against changing the rule, recalling the example of former Speaker John Boehner (R-Ohio), who resigned in 2015 rather than undergo a similar ordeal.

Other provisions in the proposed deal include expanding the number of seats available on the powerful House Rules Committee, mandating 72 hours between the posting of bills and votes on them, and trying for a constitutional amendment that would impose term limits on members of the House and Senate.

“We’ve reached a place where we think we can move that forward with some very critical changes that are going to change how this place works,” Donalds said. “Simple things like being able to read a bill before we [vote.]”

“This will change this house,” Self said after the 12th ballot. “Let’s be very clear: we will get there. We will have a strong rules package that the Republican conference will vote for.”

Despite the concessions and telling his allies they were “in a good position,” McCarthy admitted on Friday’s call that there was no final agreement with the holdouts — and there was no guarantee that any deal would sway enough of the remaining rebels to give McCarthy the gavel.

“McCarthy’s ego is what stands in the way of cleaning up the mess that the DC political consultant class has made of our country,” an anti-McCarthy House GOP staffer told The Post on Thursday evening.

“This nation was built by rebels and it’ll take rebels to save it,” the person added.

A source associated with a pro-McCarthy House office fretted late Thursday that McCarthy was most likely “f–ked” because “there are like six, seven, nine people who are never — if you believe them — going to vote for him.”

However, Donalds was more optimistic, saying the revolt was less a vendetta against McCarthy and more a challenge to the way the House has worked in recent years.

“This movement has always been secondarily about who is the speaker and primarily about reforming this place in both Republican and Democratic leadership,” he said.

As the weekend approached, it remained possible that absences could swing the result.

McCarthy supporter Ken Buck of Colorado had to miss the 12th and 13th ballots for a medical appointment, while Rep.-elect Wesley Hunt of Texas, also a McCarthy backer, went home Friday to be with his wife and their baby son. Both men were expected back in Washington in time to vote on a 14th ballot Friday night.

However, if that vote failed, Hern was expected to fly out Saturday for his mother’s funeral, altering the math once again.

Meanwhile, the mood among the GOP ranks turned decisively against Gaetz — one of the ringleaders of the so-called “Never Kevins” — with dozens of his fellow Republican members-elect walking out of the chamber in apparent frustration as he nominated Jordan for speaker ahead of the 12th ballot.

“You only earned the position of speaker of the House if you can get the votes,” Gaetz said. “Mr. McCarthy doesn’t have the votes today. He will not have the votes tomorrow and he will not have the votes next week, next month, next year. And so one must wonder … is this an exercise in vanity for someone who has done the math, taken the counts and is putting this institution through something that absolutely is avoidable?”

The impasse has brought Capitol Hill to a standstill, with a memo sent out by the House’s chief administrative officer Thursday evening warning that committees “shall only carry out core Constitutional responsibilities.” Payroll also cannot be processed if the House isn’t up and running by Jan. 13, meaning members, staffers and aides would not receive their paychecks.

With Post wires