Ebullient Republicans returned to Capitol Hill on Tuesday after elections that put them on the brink of taking control of both chambers of Congress to face critical questions about how they will wield their power — and how tight a grip President-elect Donald J. Trump will have on their new majority.
G.O.P. senators were set to make a monumental choice on Wednesday, when, for the first time since 2007, they plan to elect a party leader not named Mitch McConnell. Three men have been quietly jockeying for months to replace Mr. McConnell, the longest-serving Senate party leader in history, but some of Mr. Trump’s allies have pressed him to block the man considered to be the front-runner: Senator John Thune of South Dakota.
At the same time, Mr. Trump’s push to stack his administration with loyal members of Congress was colliding with a tough political reality for Republicans: They are running out of the bodies they need to preserve the narrow House majority they expect to hold.
With the party on track to win the House by a precariously small margin and Mr. Trump tapping two House members to serve in top national security posts, Republican leaders warned on Tuesday that they could not spare any more.
“I don’t expect that we will have more members leaving, but I’ll leave that up to him,” Mr. Johnson said, referring to Mr. Trump.
Control of the House of Representatives is still officially up for grabs, with several competitive races not yet called, but Republicans appear positioned to keep the majority by a similarly tiny edge that has made it so difficult for them to govern over the past two years. As of Tuesday afternoon, they had won control of 214 seats, and Democrats had 205. A party needs 218 seats for a majority, and most strategists expect that the G.O.P. will not end up with many more than that.
Mr. Trump has already picked Representative Elise Stefanik of New York, the No. 4 House Republican, to serve as the ambassador to the United Nations, and Representative Michael Waltz, Republican of Florida, as his national security adviser.
Representative Steve Scalise of Louisiana, the House majority leader, echoed Mr. Johnson’s concern and tried to hint that the music had stopped on Washington’s current game of musical chairs — at least when it came to his ranks.
“Hopefully no more for a little while,” Mr. Scalise said.
The developments on both sides of the Capitol reflected how Mr. Trump has bent the party to his will, with would-be Senate leaders pitching themselves as best equipped to carry out his agenda and House Republicans clamoring to join his administration.
The contenders for Senate majority leader are Mr. Thune, who is currently the No. 2 Republican; Senator John Cornyn of Texas, who has held several leadership positions in the Senate; and Senator Rick Scott of Florida, who is seen as the favorite of the party’s right flank.
Mr. Trump was expected to visit Capitol Hill on Wednesday morning, ahead of Republican leadership elections in both the House and Senate.
By Tuesday, the race to replace Mr. McConnell, who helped conservatives gain a supermajority on the Supreme Court, went into a form of heated, if genteel, overdrive.
Mr. Thune made his case in an opinion essay on Fox News, arguing that Senate Republicans need to fulfill Mr. Trump’s promises to voters in order to keep the support of a multiethnic, multiracial coalition that swept him into a second term.
“If we fail to deliver on President Trump’s priorities, we will lose their support,” he wrote. “They have trusted us with their votes. Now we have to roll up our sleeves and get to work.”
He also pitched colleagues on his plans to open up the Senate floor to more debate and amendments and said he would meet regularly with Speaker Mike Johnson.
Mr. Cornyn circulated a letter casting himself as the candidate best equipped to overhaul the chamber to get the job done for the MAGA movement.
“In order to make America great again, we must make the Senate work again,” Mr. Cornyn wrote to his colleagues. “To that end, we will reinvest in a Senate committee process to drive an aggressive legislative agenda that secures our border, reduces federal spending, boosts our economy, unleashes the nation’s energy potential and reverses bad Biden-Harris policies.”
And Mr. Scott promoted endorsements from conservative activists on social media, including arguments that he would work to keep transgender athletes out of women’s sports.
The secret-ballot election will be held Wednesday morning. Retiring senators, such as Mitt Romney of Utah, are not eligible to vote, but senators-elect, such as Tim Sheehy of Montana, are. With Republicans expecting to control 53 seats, the winning candidate must have the backing of a majority of those senators, or 27 votes, to become leader.
For months, Mr. Thune and Mr. Cornyn have been seen as having an edge in the race. Each has crisscrossed the country raising millions of dollars for other senators and shoring up votes privately.
But Mr. Scott is hoping Mr. Trump will shake up the race with an endorsement. Already, Mr. Trump’s ally, the billionaire Elon Musk, has backed the Floridian. Hard-right advisers are pushing him to weigh in against Mr. Thune, an establishment Republican who is reviled by the MAGA right.
The former president has railed against Mr. Thune in the past over his refusal to go along with Mr. Trump’s attempt to overturn the 2020 election. He has also criticized Mr. Cornyn and Mr. Thune as “weak and ineffective.”
Both Mr. Thune and Mr. Cornyn have worked to improve their relationships with Mr. Trump. Mr. Thune visited Mar-a-Lago in the spring, and spoke with Mr. Trump just days ago. Mr. Cornyn met with Mr. Trump twice in recent months and also speaks with him regularly. The two have run quiet, traditional races, working in one-on-one meetings with senators to secure votes, pitching themselves as experienced leaders who can navigate the intricacies of Congress to deliver on Mr. Trump’s legislative agenda.
Mr. Scott, by contrast, is running to appeal to the right flank of the party — and doing so publicly and online. Many in the establishment wing of the party view Mr. Scott’s time leading Senate Republicans’ campaign arm as a failure. He was blamed for a failure to recruit quality candidates, questionable spending practices and the release of a disastrous policy agenda including tax increases and the phasing out of popular entitlement programs that was quickly repudiated by his colleagues. When Mr. Trump urged him to challenge Mr. McConnell for Republican leader two years ago, Mr. Scott fell well short, receiving only 10 votes.
Most Republican senators have not publicly declared which of the three candidates they support. Privately, some are grumbling about online influencers attempting to pressure them to change their votes.
The pressure campaign for Mr. Scott has reached well beyond Washington. Outside the Nashville office of Senator Marsha Blackburn of Tennessee, just a few blocks from the famed bustling strip of downtown honky tonks, a small cluster of Trump supporters gathered on Tuesday to call on Ms. Blackburn to support Mr. Scott and disavow the other two candidates.
About 16 people wearing Trump apparel carried fluorescent signs that blared “we DON’T LIKE this Thune you’re singing Marsha!” and “et tu, Marsha?”
A spokesman for Ms. Blackburn pointed to a post on social media Monday morning in which the senator promised to “vote for the person who is best to work with President Donald Trump to begin the great American comeback.”
Senators typically resent outside intervention, even by a president, in their internal affairs, and view it as remarkable that a president would try to handpick their leader.
The last time the White House meddled in the selection of a Senate Republican leader was in 2002, when President George W. Bush and his inner circle helped push out Senator Trent Lott of Mississippi. Mr. Lott had made comments at the 100th birthday party of Senator Strom Thurmond that praised the South Carolinian’s presidential bid in 1948, when he ran as a segregationist.
The Bush team wanted Senator Bill Frist of Tennessee, a less experienced and more agreeable figure, to lead Senate Republicans, and saw the opportunity to install someone they could more easily influence. Mr. Frist, a heart transplant surgeon who had run the Republican Senate campaign operation, led the G.O.P. for four years and considered a presidential run but he was never quite able to shake the impression that he was too tightly aligned with the White House.
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