The Senate adopted the motion to proceed to a bill that would extend unemployment insurance for five months by voice-vote.

Senate Majority Leader Harry ReidHarry Mason ReidHarry Reid: 'Decriminalizing border crossings is not something that should be at the top of the list' 2020 Democrats fight to claim Obama's mantle on health care Reid says he wishes Franken would run for Senate again MORE (D-Nev.) then filled the amendment tree and filed cloture on the bill, meaning no Republican amendments will get a vote.

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Last week, the Senate voted 65-34 to end debate on the motion to proceed with the support of 10 Republicans. Final passage is expected later this week since five Republicans are cosponsoring the bipartisan measure.

However, action in the House appears unlikely because Speaker John BoehnerJohn Andrew BoehnerLobbyists race to cash in on cannabis boom Rising star Ratcliffe faces battle to become Trump's intel chief This little engine delivers results for DC children MORE (R-Ohio) has said he wouldn’t consider the Senate deal since it doesn’t include job-creating measures.

Reid said once the Senate passes the bill later this week, it would be in House’s hands.

“It’s in their hands,” Reid said Monday. “We hope they will be considerate to these struggling people.”

The Senate is using H.R. 3979, the Protecting Volunteer Firefighters and Emergency Responders Act, as the legislative vehicle for the jobless aid proposal. 

Sens. Jack Reed (D-R.I.) and Dean Heller (R-Nev.) have put together a plan that would provide retroactive benefits to more than 2 million people who lost their benefits after the program expired on Dec. 28.

Senate Republicans have blocked three other attempts to extend UI, but this time, the legislation has five Republican co-sponsors, meaning it can overcome the 60-vote threshold of a filibuster.

But there is still Republican opposition.

“The Majority Leader is steadfastly determined to pass legislation that would disincentives people going back to work,” Sen. John CornynJohn CornynThe Hill's Morning Report - Trump hews to NRA on guns and eyes lower taxes The Hill's Morning Report - Trump on defense over economic jitters Democrats keen to take on Cornyn despite formidable challenges MORE (R-Texas) said, while demanding an open amendment process to the bill. “If the Majority Leader is not interested in having an honest and open debate about how to solve this problem, then something else is driving his agenda.”

The bipartisan Senate measure would use several offsets to pay for the nearly $10 billion cost of extending the benefits, including pension smoothing provisions from the 2012 highway bill, which were set to phase out this year, and extending customs user fees through 2024.

The Senate deal also includes an additional offset allowing single-employer pension plans to prepay their flat rate premiums to the Pension Benefit Guaranty Corp. (PBGC).

The measure would also prevent millionaires and billionaires from receiving the federal benefits.

The proposal includes language to strengthen re-employment and eligibility assessment (REA) and re-employment services (RES) programs, which provide help to unemployed workers, when they enter their 27th week of benefits.

Earlier this month, the House passed H.R. 3979, which aims to exempt volunteer firefighters and EMTs from being considered full-time employees under the ObamaCare employer mandate. The Senate is using that bill as a way to send the UI extension bill back to the House. And Senate passage with Republican support could put pressure on Boehner to act.

Boehner has cited a letter from the National Association of State Workforce Agencies (NASWA) that expressed technical concerns about providing retroactive benefits, among other issues stemming from the nearly four-month lapse. 

But Labor Secretary Thomas Perez and other advocates have argued that the problems could be overcome to continue the program.

The emergency federal program kicks in once workers who have continued looking for a new job exhaust their state-level benefits, usually after 26 weeks.