The U.S. Senate voted Tuesday to move forward a bill that will restore an emergency-benefits program for 1.3 million long-term jobless people across the United States, after lawmakers allowed those benefits to expire on December 28th.

Tuesday’s “cloture motion,” which permits the measure to move ahead, barely squeaked through, and mostly along partly lines with votes coming in at 60-37. Sixty votes were needed to pass.

The Senate is expected to officially vote on the bill later this week, after which it would be sent to the Republican-led House of Representatives “where it faces stiff opposition,” as Reuters reports.

However, even before it moves to the House, Senate Republicans may still be able to negotiate changes that might limit the scope of the bill or require cuts in other parts of the budget in exchange.

Following the Tuesday vote, President Obama—who has supported the bill—said in a speech at the White House before a group of unemployed Americans, “We’ve got to make sure this recovery leaves nobody behind,” following a financial crisis that “was so devastating…there are still a lot of people who are struggling.”

If the benefits are not extended, “it will hurt about 14 million Americans over the course of this year,” including family members of the jobless, Obama warned.