Support for a compromise two-year budget deal grew ahead of a Tuesday vote in the Senate as Republicans concluded they could not allow a measure that passed the House with overwhelming bipartisan support to die in Congress’s upper chamber.

Senators Orrin G. Hatch of Utah and Johnny Isakson and Saxby Chambliss of Georgia announced their support for the measure on Monday, appearing to give it more than the 60 votes it would need to overcome a filibuster threat and bring it to a final vote, which would need only a majority. The three joined four other Republicans — Senators John McCain and Jeff Flake of Arizona, Susan Collins of Maine and Ron Johnson of Wisconsin — who have said they will vote to cut off debate.

“This agreement isn’t everything I’d hoped it would be, and it isn’t what I would have written. But sometimes the answer has to be yes,” Mr. Hatch said. “The reality is that Republicans only control one-half of one-third of government.”