Senate Majority Leader Harry ReidHarry ReidBill O'Reilly: Politics helped kill Kate Steinle, Zarate just pulled the trigger Tax reform is nightmare Déjà vu for Puerto Rico Ex-Obama and Reid staffers: McConnell would pretend to be busy to avoid meeting with Obama MORE (D-Nev.) filed cloture on a House bill that the Senate will use as a vehicle to pass an unemployment insurance extension likely by Friday.

Reid filed the motion to end debate on H.R. 3979, the Protecting Volunteer Firefighters and Emergency Responders Act, which the House passed earlier this month.

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H.R. 3979 aims to exempt volunteer firefighters and EMTs from being considered full-time employees under ObamaCare mandates. Reid will use that bill as a way to send a five-month unemployment insurance (UI) extension bill back to the House.

Since Reid filed cloture, that would set up a vote as soon as Friday but Democrats are hoping to reach an agreement to hold the vote Thursday evening.

Sens. Jack ReedJohn (Jack) Raymond ReedSenate panel moves forward with bill to roll back Dodd-Frank Army leader on waiver report: 'There's been no change in standards' 15 Dems urge FEC to adopt new rules for online political ads MORE (D-R.I.) and Dean HellerDean Arthur HellerDems look to use Moore against GOP Senate hearing shows Fed chair nominee acts the part Senate GOP votes to begin debate on tax bill MORE (R-Nev.) have put together a plan that would provide retroactive benefits to more than 2 million people who lost federal help after the program expired on Dec. 28.

The Senate has failed to pass two other UI extensions, but this time the legislation has five Republican cosponsors, meaning it could overcome the 60-vote threshold of a filibuster.

It would use several offsets to pay for the $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 Corporation (PBGC).

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

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

Despite the likelihood of Senate passage, Speaker John BoehnerJohn Andrew BoehnerJohn Feehery: A political forest fire Trump's pick for Federal Reserve chief is right choice at right time The two-party system is dying — let’s put it out of its misery MORE (R-Ohio) has said he won’t consider the Senate deal because it doesn’t include job-creating measures. But Senate passage will put pressure on BoehnerJohn Andrew BoehnerJohn Feehery: A political forest fire Trump's pick for Federal Reserve chief is right choice at right time The two-party system is dying — let’s put it out of its misery MORE to do something.

The emergency federal program kicks in once workers who continue looking for a new job have exhausted benefits, usually after 26 weeks.

— Vicki Needham contributed to this article.