J. Scott Applewhite / AP Sen. Jack Reed, D-R.I., and Sen. Jeanne Shaheen, D-N.H., react after legislation to renew jobless benefits for the long-term unemployed unexpectedly cleared an initial Senate hurdle, on Capitol Hill in Washington, Jan. 7, 2014.

The Senate voted Tuesday to move forward on a bill to reinstate long-term unemployment insurance, a week after those payments lapsed for 1.3 million Americans.

Six Republicans joined Democrats in the 60-37 procedural vote on the bill, which still needs another vote before final Senate passage. Introduced by Sen. Dean Heller (R-Nev.) and Sen. Jack Reed (D-R.I.), the measure would restart benefits for three months, but passage in the Republican-controlled House is unlikely. GOP lawmakers are calling for offsetting spending cuts to pay for the renewed benefits, something Democrats are unwilling to consider until benefits are reinstated.

The White House Council of Economic Advisers has estimated that failing to extend the unemployment benefits could cost the economy 240,000 jobs this year.

Gene Sperling, the director of the National Economic Council, said Monday that the White House would consider offsetting cuts as part of a deal to extend benefits through the rest of the year. “Let’s move quickly and pass this three-month extension now,” he said. “This will help Americans immediately, and this will give us more time to have a larger conversation about what happens after the three months are over.”

President Barack Obama is holding an event Tuesday morning with individuals who saw their unemployment benefits expire, and calling on Congress again to act swiftly to reinstate the program. House Speaker John Boehner reiterated his opposition to extending benefits without matching spending cuts in a statement after the Senate vote.

“One month ago I personally told the White House that another extension of temporary emergency unemployment benefits should not only be paid for but include something to help put people back to work,” Boehner said. “To date, the president has offered no such plan. If he does, I’ll be happy to discuss it, but right now the House is going to remain focused on growing the economy and giving America’s unemployed the independence that only comes from finding a good job.”

Before the Tuesday vote, Senate Minority Leader Mitch McConnell, who is facing a primary challenge this year, attempted to add to amendments to the unemployment insurance extension, one that would delay the health care reform law’s individual mandate for a year, and another that would restore cuts to military retiree benefits, arguing that would pay for the extension. The effort was blocked by Senate Majority Leader Harry Reid.