Speaker Mike Johnson revealed on Monday why Representative Elise Stefanik of New York has yet to have her confirmation vote to serve as ambassador to the United Nations: He cannot afford to lose another Republican vote in the House.

Mr. Johnson is under pressure this week to hold his fractious conference together to pass a budget resolution, with potentially only a single vote to spare. Ms. Stefanik, a former member of House leadership, is a team player whose support could be crucial, given the difficult math.

“If we get the budget resolution passed this week, which is the plan, then it’s possible that Elise Stefanik would go ahead and move on to her assignment at the U.N. as the ambassador there,” Mr. Johnson said on Monday during a talk at the America First Policy Institute. It was a blunt acknowledgment of the political reality of trying to pass a budget to enact President Trump’s agenda after he raided the House Republican ranks to fill out his administration.

A spokesman for Mr. Johnson said that the timing of Ms. Stefanik’s confirmation was a matter for the White House and the Senate to resolve and that the speaker was supportive of their timeline.

Senate Republican leaders have had plenty of other confirmation votes to schedule and have made it clear they are cognizant of the narrow majority in the House that puts added pressure on Ms. Stefanik to stay where she is, for now.

The Senate has been pushing through votes on Mr. Trump’s cabinet nominations at a record pace. So far, 17 cabinet members have been confirmed. Ms. Stefanik is one of just five cabinet nominees who have yet to receive a vote in the Senate.

On Monday, Mr. Johnson was plain-spoken about the fact that he simply cannot afford to lose Ms. Stefanik right now, as he strains to pass the budget plan resolution and a short-term spending bill to avert a government shutdown on March 14.

“I had 220 Republicans and 215 Democrats, and then President Trump began to cull the herd,” Mr. Johnson said. “We have a one-vote margin now — smallest in history, right? So for a big chunk of the first 100 days of the Congress, and perhaps beyond, this is not an easy task, but we’re going to get it done.”

Even with Ms. Stefanik on hand and in support, it is not at all clear that Mr. Johnson will be able to pass the budget measure, with several Republicans signaling concerns about the plan. Nor is it certain when Ms. Stefanik, who declined to comment for this article, may be cleared to move on to her next job.

For now, she is living in an awkward in-between. She is not seated on any subcommittees in the 119th Congress, though she has been attending some hearings for the committees she is still on. Meanwhile, a showdown over Ukraine is playing out at the United Nations, pitting the United States against its longtime European allies, without her.

At the Conservative Political Action Conference over the weekend, Ms. Stefanik was introduced not as a congresswoman from New York, but as the “United Nations ambassador-designate.”

“Our team is already hard at work,” she said in her remarks lauding the opening days of Mr. Trump’s administration, “as I finish my work to enact his agenda in Congress.” In his speech at CPAC, Mr. Trump referred to Ms. Stefanik as “our next ambassador to the United Nations.”

Some relief may come for Ms. Stefanik and Mr. Johnson in April, when two Trump-endorsed Republicans are expected to fill a pair of House seats that were left vacant after the departures of former Representatives Mike Waltz and Matt Gaetz of Florida.

(Mr. Waltz left to serve as Mr. Trump’s national security adviser. Mr. Gaetz resigned from the House in November after Mr. Trump nominated him to serve as attorney general, but then withdrew his name from consideration because of intense scrutiny over allegations of sex trafficking and drug use.)

The election of their successors is expected to allow Mr. Johnson a little more breathing room with his tight margin of control in the House.

Ms. Stefanik, a onetime Republican moderate turned die-hard Trump loyalist, is expected to sail through her Senate confirmation process, if and when it is scheduled. A successful confirmation vote would then start the clock on Gov. Kathy Hochul of New York, who is required by law to schedule a special election within 90 days of a declared congressional vacancy.

Some Democratic lawmakers in New York have introduced a bill that would allow Ms. Hochul to further delay the special election in Ms. Stefanik’s conservative upstate district.

Mr. Johnson is aware that once he loses Ms. Stefanik, it could be some time before he gets that vote back.

“Let’s hope that we can get it filled in time, and hope that the law is respected by Democrats in New York,” he said.

So, for now, Ms. Stefanik is stuck voting in the House.

Catie Edmondson contributed reporting.