Reed said it's not clear yet if it would attract the 60 senators necessary to pass the Senate.
Republicans have said extending jobless benefits by three months would cost $6.4 billion and have insisted it should have a revenue source so the move doesn't add to national deficits.
The new bipartisan deal would be "paid for" through something called "pension smoothing." Though it's unclear how it would happen, Reed said it is based on pension revisions that Congress passed back in 2012 to pay for a transportation funding bill.
The program's expiration hurt 1.3 million workers. Each week, another 70,000 workers have run out of state benefits with nothing to turn to, according to the National Employment Law Project. So the total number of unemployed workers eligible for benefits now hovers around 1.7 million, according to the advocacy group for unemployed workers.
The federal benefits program was first signed into law by President George W. Bush in June 2008, back when the jobless rate was 5.6%. The unemployment rate climbed to more than 10% at the height of the Great Recession in 2009, and the government extended or expanded the federal benefits 11 times into the weak recovery, most recently in January 2013.