Democratic Sen.-elect Doug Jones and his wife, Louise, step on stage Tuesday in Birmingham, Ala. His win narrows the Republicans' Senate majority to 51-49.

WASHINGTON — Weary national Republicans breathed a collective sigh of relief Wednesday, after voters knocked out their own party’s scandal-plagued candidate in deep-red Alabama. Yet the party is confronting new rounds of infighting and a suddenly shrunken Senate majority heading into next year’s midterm elections.

A semi-humbled President Donald Trump conceded that Roy Moore’s loss was not his preferred outcome. He said he “would have liked to have had the seat” and an important Senate vote as GOP lawmakers scratch for legislative victories. But he also acknowledged, “A lot of Republicans feel differently. They feel very happy about the way it turned out.”

It was easy to find establishment-minded Republicans — in and out of Washington — who cheered Moore’s loss. The prospect of a high-profile Republican senator dogged by sexual misconduct accusations unnerved the GOP.

Republican Alabama Sen. Richard Shelby said that Moore, a fiery conservative, would have brought a “radioactive” element to the Senate GOP.

“I’m relieved and I believe a lot of Republicans are relieved that Roy Moore and some of his people aren’t the face of the Republican Party that I know,” said Shelby, who cast a write-in vote for another Republican and never backed down in his opposition to Moore.

The victory of Sen.-elect Doug Jones marked a setback for Trump and political ally Steve Bannon. They had devoted time, resources and political capital to Moore in recent days, even as he faced the allegations of sexual misconduct and espoused views that alienated women, racial minorities, gays and Muslims.

Allies of Bannon dismissed the loss as little more than a temporary setback. Republicans cheering Moore’s loss, they said, would simply enrage Trump’s most loyal supporters nationwide, who already suspected some Republican leaders were trying to undermine the president’s agenda.

It’s unclear how the loss will affect the Republicans’ governing agenda.

When Jones is sworn into office, likely in early January, the GOP’s Senate majority will shrink to 51-49. That increases pressure on Republicans to push their prized $1.5 trillion tax bill through Congress before lawmakers leave town late this month, a goal they seem likely to achieve.

The narrowing majority gives extra leverage to Republicans like moderate Maine Sen. Susan Collins, who’s extracted leadership promises for accompanying legislation shoring up parts of the “Obamacare” health care law. Collins told reporters Wednesday she was confident those promises would be kept. “All you cynics in the press will have to be eating crow come Dec. 31,” she said.

Other initiatives, like a program to upgrade the nation’s infrastructure, would need 60 Senate votes to succeed. Barring a GOP effort to craft bipartisan bills, it seems unlikely nine Democrats would back such measures with elections on the horizon.