White House budget director Mick Mulvaney told CNBC on Thursday he's "cautiously optimistic" about a tentative tax deal on Capitol Hill.

House and Senate Republican negotiators, who have been scrambling to craft a compromise bill, said Wednesday they reached a framework of a deal.

The agreement "is not final yet, but we're hearing it should before midday," Mulvaney said on "Squawk Box." "The things I think they're still working on [are] the minor stuff."

"If they stay on that schedule, we could have a vote in the Senate as early as Tuesday next week, and a vote in the House as early as Wednesday," Mulvaney said.

"That would be the end of it as far as the legislative process goes," the director of the Office of Management and Budget added.

House and Senate GOP leaders are hoping to quickly pass a joint tax package and send the measure to President Donald Trump's desk before Christmas.

The president wants the "best bill we can pass," said Mulvaney, formerly a congressman from South Carolina and member of the hard-line conservative Freedom Caucus.

Trump tweeted his encouragement Thursday morning:

Republican Tax Cuts are looking very good. All are working hard. In the meantime, the Stock Market hit another record high!

On the tax reform optimism, the Dow Jones industrial average closed at a record high on Wednesday, the 68th time this year.