WASHINGTON – The Senate broke a months-long stalemate Tuesday over a plan to restore emergency jobless benefits to millions of people who have been out of work for more than six months, voting to advance the measure over Republican objections that it would add $34 billion to the nation’s bloated budget deficit.

The 60-40 vote all but assures that the bill will pass the Senate when a final vote is taken today. The measure would then go back to the House, where leaders expect to quickly approve it and send it to the White House for President Obama’s signature later this week.

Once signed, the bill would revive benefits for more than 2.5 million people whose checks were cut off when the program expired June 2. It also would ensure that up to 99 weeks of income support would be available to a broader universe of jobless workers through the end of November.

Maine Republican Sens. Olympia Snowe and Susan Collins were the only two Republicans to break ranks and vote with Democrats to end the impasse.

While jobless benefits have traditionally received bipartisan support in periods of high unemployment, the current round has been caught in a cross-fire of partisan sniping about the deficit as lawmakers position themselves for this fall’s midterm elections. In the wake of the recession, U.S. policymakers and their counterparts abroad have struggled to create jobs and bolster a sluggish recovery without adding unduly to national debt. Rising debt loads have sparked a crisis in Europe.

Pointing to growing public anxiety about U.S. debt, which now stands at more than $13 trillion, most Republicans refused to back the extension of jobless benefits unless Democrats agreed to cover its cost using unspent funds from last year’s economic stimulus package.

“There’s no debate in the Senate about whether we should pass a bill — everyone agrees that we should,” Senate Minority Leader Mitch McConnell, R-Ky., said. “What we do not support — and we make no apologies for — is borrowing tens of billions of dollars to pass this bill at a time when the national debt is spinning completely out of control.”

Obama and fellow Democrats, meanwhile, have accused Republicans of turning their backs on the unemployed while pushing to extend tax cuts for the wealthy that would increase deficits by $650 billion over the next decade.

“Our Republican colleagues … say, ‘No, you have got to pay for that, but you don’t have to pay for a tax cut for the wealthiest people in America,’ which is about 20 times as much as the unemployment insurance,” said House Majority Leader Steny Hoyer, D-Md.

Snowe said that now is not the time to hold back on jobless benefits.

“At this time of unemployment rates at 9.5 percent nationally and 8 percent in Maine, until the economy starts creating jobs — something Congress has failed to encourage thus far — I will not impede the passage of unemployments benefits by insisting that they be fully offset,” Snowe said in a statement.

“Congress will rightly move toward extending this critical safety net program and ensuring that hard-working families have access to the resources they need during these troubling times,” she said.

Collins also issued a statement: “I hope that passage of this extension will provide some much needed temporary assistance to those families who currently must rely on unemployment benefits due to the loss of jobs,” she said.

A lone Democrat, Sen. Ben Nelson of Nebraska, voted to continue the GOP filibuster. The clinching vote was cast by Sen. Carte Goodwin, D-W.Va., who was appointed Friday to replace the late Robert Byrd, who died last month at age 92.

Moments after Vice President Joe Biden swore him into office, the chamber’s newest member walked onto the Senate floor with Sen. Jay Rockefeller, D-W.Va., approached the clerk’s desk at the front of the chamber and soberly mouthed the word “aye.” Friends and family in the Senate gallery broke into applause.

“That will be a vote that helps millions of Americans,” Goodwin said afterward, adding that he was “privileged to have played a small role” in passing the legislation.

With the unemployment rate at 9.5 percent, 8.7 million people were receiving jobless benefits at the end of June. A little more than half received state benefits, which are typically available for 26 weeks. The rest were receiving extended benefits financed by the federal government, which are due to run out soon unless this bill passes. The Labor Department estimates that 2.5 million people had been cut off by the end of last week.

The bill before the Senate would extend benefits retroactively. While state laws vary, labor officials and advocates for the unemployed said some people could expect to see lump-sum payments covering lost income back to June 2. Even if the bill passes, many people will have to wait two to four weeks before checks are restored, said Rick McHugh, a staff attorney for the National Employment Law Project, which advocates for jobless workers.

“I’m sure it seems important to people in Washington, who are fighting over these budget points of order, but it doesn’t look very important to people in the real world,” said McHugh, who works in Michigan, where the jobless rate is more than 13 percent. “It’s not a pleasant process to get calls from these folks who are losing their houses and losing their health insurance and taking their kids out of college and making the choices people are being forced to make in this economy.”

Passage of the jobless benefits bill would mark a modest victory for Obama and congressional Democrats, who have been struggling since February to push through a significant extension of the program. The provision was originally part of a much larger package of fresh spending on the economy, but Democrats have been forced repeatedly to pare it back as conservative Democrats joined Republicans in arguing that the nation could ill-afford another big hike in the national debt.

Democrats have dropped from the bill an extension of $25-a-week bonus payments that were added to unemployment checks under last year’s stimulus package, and have little hope of extending subsidies that pay up to 65 percent of COBRA health insurance premiums for the unemployed.

Obama’s push for billions of dollars in state aid has also been scaled back, and Senate Democrats were in talks with Republicans late Tuesday about ditching Obama’s proposal to increase lending to small businesses from another pending initiative.