updated 5:15 p.m.

With jobless aid poised to expire for 1.3 million Americans this weekend, a bipartisan team of senators is proposing a short-term extension of unemployment benefits that will come to the floor as soon as Congress returns in January 2014.

Sens. Jack Reed, a Rhode Island Democrat, and Dean Heller, a Nevada Republican, are proposing a bill that would extend unemployment benefits for three months.

“To cut it off this way is both wrong from a principle, what we should stand for as a nation, and from a very sound, practical economic perspective,” Reed said on a Thursday conference call.

The $6 billion proposal proposes to maintain aid for the long-term unemployed, who would have their benefits restored retroactively, while buying legislators more time to work out a longer extension. The legislation is expected to come to the Senate floor on Jan. 6, Reed said.

“My job search is my full time job. I’m sick and tired of people insinuating that folks in my situation are not looking for jobs,” said Deborah Barrett, a 57-year-old accounting professional from Rhode Island who has been out of work since February. Barrett, who was on the conference call with Reed, takes care of her elderly mother and doesn’t know how she’ll continue to support her family after her federal benefits expire this weekend. “I will do whatever I have to do—it’s petrifying,” she said.

Most Republicans oppose the extension of federal benefits—which kick in after state jobless aid expires—arguing that they increase dependency on the government and are unnecessary since the job market has improved .”Does it make sense for our country to borrow money from China to give it to the unemployed in America? That is weakening us as a country,” Sen. Rand Paul told NBC News.

A poll from Hart Research Associates, a Democratic polling firm, showed that extending the jobless benefits is broadly popular. About 55% want Congress to continue them, while about 33% agree they should be allowed to expire, according to the survey, commissioned by the National Employment Law Project, an advocacy group.

During the negotiations over the budget deal, which President Obama signed on Thursday, House Speaker John Boehner said that he would be willing to consider an extension of unemployment benefits, provided that it was paid for. But the provision did not make it into the deal worked out by Sen. Patty Murray and Rep. Paul Ryan, with Democrats resigned to resuming the fight in 2014.

The Reed-Heller proposal does not include offsets. Rep. Sandy Levin, the highest-ranking Democrat on the House Ways and Means Committee, said the emergency nature of the benefits should make payfors unnecessary. With 1.3 million losing their benefits immediately, and another 1.9 million in the following six months, “that’s like being hit by an economic hurricane,” Levin said on the conference call. “That’s the reason why in the past, there hasn’t been a payfor.”

Both Reed and Levin said they’d be open to discussing offsets to pay for a further extension of unemployment benefits, as both Democrats are ultimately hope the federal aid will continue through the end of 2014.

But the recent budget negotiations have shown just how difficult that will be. The small-ball budget deal was made possible only because Ryan and Murray managed to scrape together odds and ends that avoided raises taxes or making major entitlement cuts. Given those self-imposed constraints, finding additional funding to pay for unemployment benefits won’t be easy—even if Democrats managed to convince more Republicans to support the measure in the abstract.

And other pressing legislation could quickly overtake the issue in early 2014. While Congress has passed a budget framework, establishing overall levels of spending, it still needs to pass a separate bill to appropriate the money to avoid a government shutdown on January 15. The government is also expected to hit the debt ceiling again in early February, with top Republicans already vowing to extract something in return for raising the borrowing limit.

And that’s not to mention the ongoing fight over Obamacare, which occupied most of Congress’s attention in the weeks leading up to the Christmas recess. “It’s true there were other major, major issues, and at times they seemed to be overshadowing this,” Levin said of the expiring unemployment benefits. “But it’s not too late to act.”

Friday morning, Obama phoned Senators Reed and Heller to say he supported their proposal, and that he’d ”push Congress to act promptly and in bipartisan fashion to address this urgent economic priority,” said a statement from the White House.

Close video Dem Rep: Expiration of jobless benefits an ‘emergency’ Rep. Sheila Jackson Lee joins Craig Melvin to discuss the expiration of long-term unemployment benefits for 1.3 million Americans. Rep. Sheila Jackson Lee joins Craig Melvin to discuss the expiration of long-term unemployment benefits for 1.3 million Americans. share tweet email Embed