The Senate voted 61 to 35 Thursday afternoon to move forward with a vote on a bipartisan deal to extend unemployment benefits, a bill expected to pass with a simple majority Monday.

The Senate bill would renew federal unemployment benefits for the long-term jobless, allowing for retroactive payments to go to more than 2 million Americans whose benefits expired in late December.

"We have cleared the last major procedural hurdle," said Sen. Jack Reed, (D-R.I.) at a news conference after the vote. "This represents a bipartisan approach to a critical problem that faces at this point about 2.8 million Americans and their families."

The unemployment extension deal was brokered by Reed and Sen. Dean Heller — who represent the two states with the highest levels of unemployment in the country — but is expected to find a difficult pathway forward in the House.

"Hopefully the House will take it up in its current form," Heller said. "I've told my staff: Get me a meeting with Speaker Boehner and lets see what we can do to motivate them to move this legislation."

Under the federal unemployment system, someone who loses a job typically receives unemployment benefits from the state for 26 weeks. But in 2008,  Congress voted to provide additional aid that made checks available for as long as 99 weeks in the hardest-hit states. Last year, lawmakers cut the maximum benefit to 73 weeks. Then, at the end of December, Congress let federal aid lapse altogether.

That cut aid to 1 million people en masse in December, and the ranks of those no longer receiving benefits has been growing by about 72,000 a week, according to the National Employment Law Project, which lobbies on behalf of the jobless.