The Senate voted Tuesday to advance legislation that would restore emergency jobless benefits to millions of people who have been out of work for more than six months, finally overcoming Republican objections that the measure would add to the nation's bloated budget deficit.

On a vote of 60-40 that ended a months-long stalemate, the Senate agreed to move to a final vote on the $34 billion measure later Tuesday. The bill would then go back to the House, where leaders hope to approve it Wednesday and send it on to the White House for President Obama's signature.

If approved, the bill would restore benefits to more than 2.5 million people who have seen their checks cut off since the emergency program expired June 2. It would also provide up to 99 weeks of income support to a broader universe of jobless workers through November.

Two Republicans -- Maine Sens. Olympia J. Snoweand Susan Collins -- voted with Democrats to break the impasse. But the clinching vote was provided by Sen. Carte Goodwin (D-W.Va.), who was appointed to replace the late Robert C. Byrd after his death last month.

Moments after Vice President Biden swore Goodwin into office, the chamber's newest member walked onto the Senate floor accompanied by Sen. John D. Rockefeller IV (D-W.Va.), approached the clerk's desk at the front of the chamber and voted "aye." It was an unusually meaningful first vote for any senator.

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

One Democrat, Sen. Ben Nelson of Nebraska, voted against the measure, agreeing with Republicans that extension of the emergency-benefit program, first approved during the Bush administration and extended in last year's economic stimulus bill, should be paid for.

Some Republicans opposed extending benefits, arguing that doing so would encourage people to postpone looking for work. But Senate Minority Leader Mitch McConnell (R-Ky.) said the measure could have been approved weeks ago if Democrats had agreed to cover its cost.

"There's no debate in the Senate about whether we should pass a bill -- everyone agrees that we should," McConnell said. "This debate is about whether, in extending these benefits, we should add to the debt or not."

That battle, first engaged in late February, has dragged on for months and forced Democrats repeatedly to pare back their plans for helping unemployed workers and stimulating a sluggish economy. Democrats have dropped a $25 a week bonus payment added to unemployment checks in last year's stimulus package, and abandoned plans to extend subsidies that pay up to 65 percent of COBRA health insurance premiums for unemployed workers.

"It shouldn't take a supermajority to help families afford the bare necessities while unemployment is rising," said Senate Majority Leader Harry M. Reid (D-Nev.). "It shouldn't take the slimmest of margins to do what is right."