Republicans are likely to back the tax deal announced Monday night by President Obama, a top Senate Republican said Tuesday.

Sen. Lamar Alexander (R-Tenn.), the chairman of the Senate Republican Conference, said he expected most members of his party to vote for the compromise proposal, which calls for an extension of current income tax rates over the next two years. In exchange, other tax breaks will be extended for the short term, and unemployment benefits will be extended for 13 months.

"I think it'll have substantial Republican support, and I hope that the Democrats join us," said Alexander, the third-ranking GOP senator, on Fox News.

Other Republicans have been more tentative in fully endorsing the deal, which is seen as more of a concession to the GOP than anything else.

Senate Minority Leader Mitch McConnell (R-Ky.) said his members would "review this bipartisan agreement," while a spokesman for House Speaker-designate John Boehner (R-Ohio) said that the party "look[s] forward to discussing this proposal with House Republican Members and the American people."

It's still conceivable that some Republicans might break with leaders and decide to vote down the tax deal, especially over concerns about the spending attached to it.

Rep. Michele Bachmann (R-Minn.), the leader of the House Tea Party Caucus, said that conservatives could scuttle the tax deal over spending.

"I don't know that Republicans would necessarily go along with that vote. That would be a very hard vote to take," Bachmann said Monday.