Todd Blanche’s nomination to become attorney general suffered a severe blow on Thursday when President Trump threatened to withdraw Mr. Blanche’s name rather than scale back a tax immunity deal that would benefit himself and his family, as demanded by two Republican senators.

Mr. Trump’s threat, posted on social media, followed 24 hours of frenetic and fruitless negotiations among Mr. Blanche, the White House and the two senators, John Cornyn of Texas and Thom Tillis of North Carolina, who are not returning to Congress next year.

“I have no objection to temporarily withdrawing Todd’s name, if they do not do the right thing, and putting him back after Cornyn and Tillis are out of office,” Mr. Trump wrote, in a fight that has exposed the limits of his power over Congress.

The White House had not formally withdrawn the nomination as of midday Thursday, according to two people familiar with the situation. The White House has given no guidance on when, or even if, Mr. Trump will follow through.

Mr. Cornyn and Mr. Tillis object to a deal negotiated by Mr. Blanche and Mr. Trump’s personal lawyers to resolve a lawsuit the president had filed against the I.R.S. The deal gave Mr. Trump, his family and his businesses broad immunity against I.R.S. audits, potentially saving them at least $100 million in penalties. Democrats and even some Republican lawmakers criticized the deal as a giveaway to the Trump family. The two senators want to put limits on the deal in order to advance Mr. Blanche’s nomination, but the administration has refused.

Mr. Blanche cannot afford a single Republican defection on the Senate Judiciary Committee if he hopes to advance his confirmation to the Senate floor. The opposition of Mr. Cornyn and Mr. Tillis leaves him two short, forcing the committee to scrap its scheduled vote on Thursday.

Mr. Blanche, the president’s former top defense lawyer, can remain as acting attorney general indefinitely.

But the fact that some Republicans, emboldened by Mr. Trump’s declining popularity and alarmed by his lack of concern for their own political fortunes, even temporarily derailed a flagship nominee raised questions about Mr. Trump’s capacity to sustain the dominance over congressional Republicans that has allowed him to exert unmediated control over the department.

Mr. Trump’s threat is unusual, in at least two respects. First, there is no guarantee that Republicans will maintain their commanding majority in the upper chamber, or be more willing to accede to his demands after the midterms. Second, pulling Mr. Blanche’s nomination, even temporarily, would demonstrate Mr. Trump’s willingness to advance his personal interests over the institutional stability embodied by a Senate-confirmed attorney general.

The tax deal, tacked onto a Blanche-backed plan to create a $1.8 billion fund to compensate people who said they were victims of unfair prosecution by the government, pushed Senate Republicans to the brink. The fund raised the possibility of the government making gigantic payments to the people who stormed the Capitol on Jan. 6, and forced Mr. Blanche to declare it was dead, even as he declined to put that commitment in writing. But he gave no ground on the tax immunity deal.

At a closed-door meeting in May, several Republican senators browbeat Mr. Blanche for signing off on a wide-ranging agreement they saw as a vast conflict of interest that would be perceived by voters as an effort to line the pockets of Mr. Trump, his family and his political allies.

Mr. Trump nonetheless cast the objections as a personal vendetta against him. He accused Mr. Cornyn and Mr. Tillis of a sour-grapes revolt aimed at punishing him for withholding his kingmaker endorsement in their contested Republican primaries. Mr. Tillis decided not to seek another term after repeated public attacks from the president, while Mr. Cornyn lost his re-election bid to a challenger backed by Mr. Trump.

“John Cornyn, of Texas, and Thom Tillis, of North Carolina, both of whom I refused to Endorse, and whose political careers have been ended by my action, are refusing to vote for this Great Nominee, who will remain, in any event, as Acting,” the president wrote on Truth Social.

Mr. Cornyn quickly pushed back, suggesting that he and Mr. Tillis represented a much larger group of Senate Republicans who had reservations about the implications of the tax deal, but could not incur the political risk to publicly oppose the White House that their status afforded them.

“There are more than just two people who have reservations about the weaponization fund and about the scope of the settlement decree,” Mr. Cornyn said. “And you know, after the midterms, who knows who’s going to be the next United States senator from North Carolina or Texas?”

“This is not popular,” Mr. Tillis said at the Capitol. “The president’s not winning on this issue. It is killing some of our candidates because they can’t explain it. And now, it looks like they weren’t being honest when they said it was inoperative.”

Before Mr. Trump’s social media post, Mr. Cornyn told reporters that he believed “higher-ups at the White House” were blocking efforts to reach a deal to modify the settlement in Mr. Trump’s lawsuit against the I.R.S.

Mr. Cornyn said he had sent a proposal to the Justice Department that included limits on the provision in the settlement protecting Mr. Trump from I.R.S. audits, a guarantee he said he needed before voting to advance Mr. Blanche’s confirmation.

“I thought we were pretty close to landing the plane last night,” Mr. Cornyn said. “But this morning there’s been some more complications.”

Doubling down on his critique of the White House, Mr. Cornyn said pulling Mr. Blanche’s nomination would not resolve the president’s problems over the Senate confirmation. “I think the D.O.J. needs a Senate-confirmed attorney general,” he said. “And Todd Blanche is probably about as good as we’re going to get. I just think they need to do what Todd Blanche swore that this deal meant and they need to put that in writing.”

Senator John Kennedy, a Louisiana Republican who serves on the Judiciary Committee, said on Thursday that he was not surprised that the president said he may temporarily pull Mr. Blanche’s nomination.

“Obviously, the White House did not want to comply with what Cornyn and Tillis wanted,” he said.

The tax provision, signed by Mr. Blanche and dated May 19, appeared to be twofold. It ordered the I.R.S. to drop any criminal investigations or audits of Mr. Trump, his family and their businesses, as well as any “affiliated individuals.” It also told the agency to not start any new investigations into tax returns they had already filed.

Mr. Cornyn wants Mr. Blanche, in writing, to limit who receives protection. Only Mr. Trump, two of his sons and the Trump Organization should be subject to the order, Mr. Cornyn has said. That would mean that other members of Mr. Trump’s family beyond Don Jr. and Eric Trump, as well as other companies they work with, would no longer be potentially covered by Mr. Blanche’s order.

Mr. Cornyn also wants Mr. Blanche to clarify that the I.R.S. must abandon only audits of past tax returns — meaning that Mr. Trump could still be audited in the future — and state that the I.R.S. is the only agency bound by the order.

During his confirmation hearing this month, Mr. Blanche, under questioning by Mr. Cornyn, verbally conceded all three points. But, so far, he has been unwilling to reflect that in writing.

Even with Mr. Cornyn’s requested changes, the audit protection for Mr. Trump would still be an unprecedented gift to a sitting president, effectively exempting him from the legal requirement for all Americans to comply with the nation’s tax laws — or face I.R.S. scrutiny.

Mr. Trump and his family members have aggressively avoided taxes for years, repeatedly facing I.R.S. audits as a result. Just one known dispute with the agency, which was still going on before Mr. Blanche’s order, could have cost Mr. Trump more than $100 million if the I.R.S. prevailed.

Andrew Duehren, Maggie Haberman and Olivia Diaz contributed reporting.