WASHINGTON — With a GOP filibuster safely broken, the Senate is poised to pass legislation restoring jobless benefits for millions of people unable to find work in the frail economic recovery.

Wednesday’s vote is a formality after the Democratic-controlled Senate voted 60-40 Tuesday to move ahead on the bill. The measure would then go to the House for one final vote and on to President Barack Obama later this week.

At issue are payments averaging $309 a week for almost 5 million people whose 26 weeks of state benefits have run out. Those people are enrolled in a federally financed program providing up to 73 additional weeks of unemployment benefits.

About half of those currently eligible have seen their benefits cut off since funding expired June 2. The jobless benefits are a lifeline to millions of people struggling to find work in what has so far been a largely jobless recovery.

“I can’t tell you how relieved we will be when Congress passes this. We have in Pennsylvania about 200,000 people who have lost their unemployment compensation coverage because of their inaction,” said Pennsylvania Secretary of Labor and Industry Sandi Vito. “Folks need this money for their mortgages, for food, and so our goal is to get them their payments as quickly as possible.”

The filibuster-breaking vote came moments after Democrat Carte Goodwin was sworn in to succeed West Virginia Democrat Robert Byrd, who died last month at 92. Goodwin was the crucial 60th senator needed to defeat the Republican filibuster. The Senate gallery was packed with Goodwin supporters, who broke into applause as he cast his “aye” vote.

Republicans say they support the benefits extension. But with the exception of Maine GOP moderates Olympia Snowe and Susan Collins, who voted with Democrats Tuesday, they insist any benefits be financed by cuts to programs elsewhere in the $3.7 trillion federal budget.

The election-year battle has been amplified by the White House and Democrats, who are emphasizing the plight of the unemployed while arguing that putting money in the pockets of jobless families would also boost economic revival.

“This bill is about jobs because unemployment insurance goes to people who will spend it immediately,” said Sen. Max Baucus, D-Mont. “That would increase economic demand. And that would help support our fragile economic recovery.”

Many Republicans have voted in the past for deficit-financed benefits extension – including as recently as March and twice in 2008, during the Bush administration. But now they are casting themselves as standing against out-of-control budget deficits, a stand that’s popular with their core conservative supporters and the tea party activists whose support they’re courting in hopes of retaking control of Congress.

“We’ve repeatedly voted for similar bills in the past. And we are ready to support one now,” said Senate Minority Leader Mitch McConnell, R-Ky. “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.”

The measure would reauthorize the extended benefits program through the end of November, providing payments to millions of people who’ve been out of work for six months or more. Maximum benefits in some states are far higher than the $309 a week nationwide average payment. In Massachusetts, the top benefit is $943 a week; in Mississippi, it is $235.

Tuesday’s action capped months of battling over the jobless benefits extension, which started in February as just one piece of a broader jobs package that included many other provisions, such as restoring expired business tax breaks and helping state governments pay their bills.

That broader measure advanced in fits and starts – including a measure that passed the Senate in March that would have added $100 billion to the deficit. But the sands shifted and it collapsed in June despite being cut back considerably.

Senate Majority Leader Harry Reid, D-Nev., then pressed a bare-bones jobless benefits measure – only to fall one vote short because of Byrd’s death.

The White House has signaled it may seek another renewal of benefits in November if unemployment remains painfully high.