A total of 60 votes were needed to break the threat of a filibuster by some Republicans. A dozen Republicans joined 55 Democrats voting to end debate. Final approval of the spending blueprint is expected by a simple majority of the 100 senators later.
The New York Times said Republican support was strong, surprisingly so after days of political posturing and Tea Party opposition.
The budget deal, which sailed through the House Thursday on a 332-94 vote, calls for defense and non-defense spending to rise to $1.012 trillion this fiscal year from the $967 billion already slated. The increase eases mandatory across-the-board spending cuts known as sequestration.
Spending next fiscal year, starting Oct. 1, would rise to $1.014 trillion from $995 billion.
The measure also phases in revenue hikes and spending offsets that lawmakers promise will lead to a net $23 billion deficit reduction over a decade.
Several liberal Democrats have said they are unhappy the deal doesn't extend long-term unemployment insurance to millions of out-of-work Americans.
Sen. Lindsey Graham, R-S.C., acknowledged that change had to come when military pay and benefits occupy 56 percent of the Defense Department's budget, the Times said. He was joined by Sens. Kelly Ayotte, R-N.Y., and Roger Wicker, R-Miss.
Graham said just before the vote, ""The truth of the matter is, we're probably going to lose this fight, but we're going to win this war," he said just before the vote.
Republican Sens. Orrin Hatch of Utah and Johnny Isakson and Saxby Chambliss of Georgia said Monday they supported the budget deal worked out by House Budget Committee Chairman Paul Ryan, R-Wis., and Senate Budget Committee Chairman Patty Murray, D-Wash., and would vote to cut off debate on it.
"I think it's important that we have this agreement," McCain told CBS's "Face the Nation" Sunday.
"This agreement isn't everything I'd hoped it would be, and it isn't what I would have written," Hatch said in a statement Monday.
"But sometimes the answer has to be yes," he said. "The reality is that Republicans only control one-half of one-third of government. Ultimately, this agreement upholds the principles conservatives stand for and, with Democrats controlling the White House and the Senate, it is the best we could hope for."