Senate Homeland Security Committee member Sen. Kelly Ayotte, R-N.H., speaks with reporters as she leaves a closed committee hearing on Secret Service agent behavior, on Capitol Hill in Washington, Tuesday, April 1, 2014. (Cliff Owen/AP)

The Senate voted 59 to 38 Monday in favor of a bill that would restore federal funding for extended unemployment benefits for 2.8 million Americans who are considered “long-term unemployed.”

The deal, carried by Democratic senators but struck with the support of several prominent Republicans — including Sens. Rob Portman (Ohio), Kelly Ayotte (N.H.) and Mark Kirk (Ill.) — came on the Senate’s fourth vote on a bill to renew the benefits.

The measure, which would restore the federal funding that pays for unemployment insurance after state-sponsored insurance ends after 26 weeks, easily passed the Senate on Monday evening and now heads to the House — where Republican House Speaker John A. Boehner (Ohio) has repeatedly signaled that it is unlikely to come up for a vote.

“If our bill was put up for a vote in the House, there is no question it would pass. Contrary to right-wing talking points, many of the people who would benefit [from] this bill are out of work through no fault of their own, and have been knocking on doors and going online looking for a job for months or even years,” Sen. Charles E. Schumer (D-N.Y.) said in a statement before the Senate vote. “The House needs to extend unemployment benefits to millions of Americans right now, without attaching extraneous issues that are merely an attempt to score political points.”

Republican House leaders have repeatedly stated their opposition to the Senate bill, noting that they do not want to bring any unemployment legislation to the floor for a vote unless it includes job-creation provisions.

But House Democrats say they intend to force the issue.

The starting point for Democrats is reenlisting the support of a group of moderate Republicans — Reps. Joseph J. Heck (Nev.), Christopher P. Gibson (N.Y.), David Joyce (Ohio), Frank A. LoBiondo (N.J.), Michael G. Grimm (N.Y.), Peter T. King (N.Y.) and Jon Runyan (N.J.) — who in December signed a letter to Boehner asking the Republican House leadership to consider a temporary extension to the unemployment benefits.

House Democrats and Republican allies have also begun wearing stickers while they are in the Capitol that include the number of long-term unemployed in their state. House aides say LoBiondo is leading an effort to send another letter, which could include new co-signers.

One of the major variables is what, if any, political capital President Obama is willing to expend toward passage of unemployment insurance extension in the House.

In a statement after the Senate vote, Labor Secretary Thomas Perez urged the House to act.

“Every day of congressional inaction is another day of struggle for the 2.2 million people who are out of work through no fault of their own,” Perez said. “I’ve heard from governors and labor secretaries from both parties who are ready and able to implement this vital program for their residents. I encourage the House to vote and send this legislation to President Obama’s desk for his signature.”

Were Obama to commit to pressing the issue — perhaps through a series of speeches like the ones he has given around the country in recent weeks about minimum wage legislation — it could ramp up pressure on House Republicans, especially those facing reelection in states with high unemployment.

Republican aides agree that an aggressive campaign by the White House has the potential to drastically change the legislative dynamic.

Democratic aides say that the executive branch could force the issue even without a full-on effort by the president. They say that a series of speeches by top Obama administration officials on employment, the economy and a need to strengthen the social safety net could be enough.

Another option is that House Republicans could take up a bill like one proposed by Rep. Charlie Dent (R-Pa.) that would link the unemployment insurance extension to issues including the 40-hour workweek, the Keystone pipeline, and medical-device tax measures.

But Dent said he had no commitment from the House leadership to move the bill.