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The White House had not formally withdrawn the nomination as of midday Thursday, according to two people familiar with the situation.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 narrow the deal in order to advance Mr. Blanche’s nomination, demanding that he put in writing what he acknowledged at his confirmation hearing: that the provision applies to only Mr. Trump, two of his sons and the Trump Organization, and that it would be limited to audits of past tax returns. But the administration so far has refused.