WASHINGTON — With 1.3 million jobless workers losing their benefits Saturday, Democrats on Capitol Hill are pushing for a three-month extension that is slated to face a key procedural vote as soon as next week.

The bill, introduced by Sens. Jack Reed, D-R.I., and Dean Heller, R-Nev., would prolong emergency unemployment benefits that have been in place since the depths of the recession in 2008.

Reed said the bill would offer retroactive benefits. He added that his priority is securing a filibuster-proof majority during a Senate vote scheduled for Jan. 6.

“I’m now taking it step by step. The first step is the procedural vote, where we need 60 votes,” Reed said Saturday. “A lot of it is going to be a reflection of what my colleagues are hearing from back home.”

On Friday, President Barack Obama called Reed and Heller to offer his support for their bill.

“The President said he was pleased that they were working in a bipartisan fashion to address a problem that will directly affect 1.3 million Americans during the holidays and have a negative impact on the nation’s economic growth and job creation,” White House spokesman Josh Earnest said in a statement.

The program’s cost for the first three months of 2014 would be around $6.5 billion, according to Reed’s spokesperson, Chip Unruh. The tab for the entire year would be roughly $24 billion.

Reed and Heller have not proposed any cuts to the federal budget that would pay for the extension. The lawmakers say they want to buy more time as they look for ways to pay for a full-year renewal of the program, possibly by eliminating certain corporate tax breaks.

An estimated 4 million people have been jobless for at least 27 weeks — the highest long-term unemployment rate since World War II.

Typically, the federal government works with state governments to provide up to 26 weeks of unemployment insurance to jobless Americans. Since a 2008 law signed by President George W. Bush, though, workers who exhaust those benefits have been eligible for additional weeks of benefits. Until now, Congress has repeatedly reauthorized this benefit.