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 ReidMcConnell not yet ready to change rules for Trump nominees The Hill's Morning Report — Sponsored by CVS Health — Trump’s love-hate relationship with the Senate Trump to press GOP on changing Senate rules MORE (D-Nev.) then filled the amendment tree and filed cloture on the bill, meaning no Republican amendments will get a vote.

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 BoehnerGOP revolts multiply against retiring Ryan Can Jim Jordan become top House Republican? Tensions on immigration erupt in the House GOP 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 CornynOvernight Finance: House panel to take up bill toughening review of foreign deals | Trump acknowledges Cohen payment on disclosure form | Officials set for new round of China trade talks Groups urge Senate panel to reject Trump's pick for Louisiana-based appeals court House panel will consider bill to boost foreign investment review powers next week 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.