WASHINGTON — Neera Tanden, President Biden’s nominee to head the Office of Management and Budget, suffered a significant setback on Monday as two moderate Republicans said they would not support her nomination, potentially dooming her chances for confirmation.

The statements of opposition from Senators Susan Collins of Maine and Mitt Romney of Utah, two Republicans with a professed willingness to work with the Biden administration, further winnowed Ms. Tanden’s chances in an evenly divided Senate. Three senators in four days have announced plans to vote against her, after Senator Joe Manchin III, Democrat of West Virginia, became the first to publicly oppose her confirmation.

A White House official said on Monday that the administration continued to stand behind Ms. Tanden’s nomination, but her path to confirmation was increasingly narrow. Her failure to win confirmation would be the first casualty for Mr. Biden, who has so far been able to win Senate support for several other cabinet picks, though many nominees have yet to face full Senate votes.

Ms. Tanden’s fate consumed the White House on Monday, as continued questions about her history of attacking both Republicans and progressive Democrats threatened to undercut Mr. Biden’s promise to bring a unifying tone to Washington. When pressed repeatedly about whether Mr. Biden had any problems with Ms. Tanden’s social media practices, Jen Psaki, the White House press secretary, avoided answering directly and focused on the nominee’s qualifications.

“The president would not have nominated her if he did not think she would be an excellent O.M.B. director,” Ms. Psaki said at a White House news briefing, adding that she disagreed with critics who had concluded that Ms. Tanden was not the right choice for the job.

Ms. Tanden’s nomination is endangered largely because of statements she made in the past, particularly on social media, in which she leveled partisan and often personal criticism at lawmakers in both parties. Republican lawmakers have increasingly questioned whether she would be able to bring the kind of “unity” that Mr. Biden has promised.

Ms. Collins and Mr. Romney pointed to Ms. Tanden’s approach to social media — namely, a relentless stream of critical tweets that were quietly deleted before her confirmation hearings this month — as reason for their opposition. Ms. Collins was among those on the receiving end of Ms. Tanden’s online wrath, which extended to both lawmakers and activists in both parties.

“Her past actions have demonstrated exactly the kind of animosity that President Biden has pledged to transcend,” Ms. Collins said, adding that Ms. Tanden “has neither the experience nor the temperament” for the position. The nominee’s decision to quietly cleanse parts of her social media feed, Ms. Collins concluded, “raises concerns about her commitment to transparency.”

Shortly after that statement, a spokeswoman for Mr. Romney confirmed the senator’s opposition, noting that “he believes it’s hard to return to comity and respect with a nominee who has issued a thousand mean tweets.” It was unclear whether that would be enough to pull the nomination.

“Clearly, Senator Manchin’s public statement makes this a challenge,” Senator Richard J. Durbin of Illinois, the No. 2 Democrat, told reporters on Monday. “We need to find support on the Republican side of the aisle to make up for that vote.”

While at least one Republican, Senator Lisa Murkowski of Alaska, declined to say whether she had made a decision on Ms. Tanden’s nomination, others echoed the opposition. Among them was Senator Rob Portman, an Ohio Republican who served as the director of the Office of Management and Budget during the George W. Bush administration.

“I think at some point, she’s just burned her bridges,” Senator John Cornyn, Republican of Texas, told reporters. “So I’m sure she’ll have a great future doing something else, but not as O.M.B. director.”

So far, the White House has indicated that it remains behind Ms. Tanden. Ms. Psaki said in a statement after Ms. Collins’s decision that Ms. Tanden “is an accomplished policy expert” and that the administration planned “continuing to work toward her confirmation through engagement with both parties.”

Ms. Psaki reiterated that support at a news briefing on Monday afternoon, calling Ms. Tanden “a brilliant policy expert with experience at the highest levels of government.” She added that the nominee had a wide range of support and that she had “worked with partners across the ideological spectrum.”

“The president nominated her because he believes she’d be a stellar O.M.B. director,” Ms. Psaki said. When asked if the White House continued to believe that Ms. Tanden had a path to confirmation, Ms. Psaki replied, “we do.” She also said the White House had been “working the phones” and had called Republicans and Democrats over the weekend to try to secure support.

Ms. Tanden did not immediately respond to a request for comment about whether she planned to remain in the running for the job. She had apologized to lawmakers during her confirmation hearings, saying she regretted her tone and vowing to work with members of both parties.

Mr. Biden nominated her before Democrats wrested back control of the Senate in January, surprising lawmakers and aides given her history of inflammatory statements. Ms. Tanden’s prospects have long appeared tenuous in light of her criticism of Republicans and progressive Democrats after serving as an adviser to Hillary Clinton during her bid for the presidency in 2016.

At her confirmation hearings this month before two Senate committees, Ms. Tanden apologized multiple times for personal attacks that she had leveled on Twitter over the years. She said she had deleted more than 1,000 tweets shortly after the election in November because she regretted her tone.

Although she promised to bring a radically different approach to her communication style if she assumed the job of budget director, Ms. Tanden was confronted by Republicans with her comments about “Moscow Mitch” — a reference to Senator Mitch McConnell of Kentucky, the Republican leader — and her suggestion that “vampires have more heart than Ted Cruz,” the Republican senator from Texas.

Ms. Tanden does have the backing of the U.S. Chamber of Commerce, but conservative political action groups and liberal activists have mobilized against her nomination, suggesting that she will be hard pressed to find support from other Republicans.

“Neera Tanden is an architect of Obamacare, cheerleader for the Green New Deal and advocate for socialism in America,” David M. McIntosh, the president of the Club for Growth, said this month. “Any senator that cares about working with O.M.B. to grow the economy — not destroy it — should vehemently oppose this nomination.”

Republicans were not the only ones who confronted Ms. Tanden. Senator Bernie Sanders of Vermont, the chairman of the budget committee, asked her to “reflect” on some of the things she had said about him and his progressive allies over the years.

“There were vicious attacks made against progressives, people who I have worked with, me personally,” Mr. Sanders said at the hearing. He also grilled her about the millions of dollars of corporate donations that she had helped facilitate as the chief executive of the Center for American Progress, a liberal think tank. The senator added that he had concerns about whether Ms. Tanden would be beholden to business interests if confirmed.

Mr. Sanders has not said publicly whether he will vote for Ms. Tanden.

Progressives sought to further derail the nomination on Monday.

The activist group RootsAction coordinated a Twitter “storm,” with images and hashtags to encourage senators, including Mr. Sanders, to reject Ms. Tanden. The group pointed to the donations from foreign governments that the Center for American Progress received and her previous comments supporting cuts to social safety net programs.

“Tanden has become known as one of the most prominent anti-progressive voices of the neoliberal establishment,” the group said in a background document.

But some Democrats argued that after voting against Trump administration nominees they deemed unqualified and watching Republicans dodge questions about social media posts, Mr. Biden should not withdraw Ms. Tanden’s nomination.

“She’s qualified,” said Senator Jon Tester, Democrat of Montana. “Anybody who can get both the left and the right mad has got to be qualified.”

Ms. Tanden’s nomination did win support from some progressive groups that feared that Mr. Biden would pick someone with deep corporate ties for the job. Jeff Hauser, the founder of the Revolving Door Project, said on Monday that it was surprising that senators would block a nominee because of her tone on Twitter.

“The last decade has seen mediocre or worse cabinet appointments rubber-stamped by the Senate with regularity,” he said. “It is unconscionable that the rare exception to that norm might be based on feelings hurt by imprudent tweets and suggests that senators vote more on egos than substance.”