Democratic leaders in the Senate are planning to fast-track legislation to extend unemployment insurance, a move that would provide a lifeline tomore than a million jobless Americans who lost their benefits five days ago.

The bipartisan bill provides a three-month extension the the federal benefits program, a temporary fix designed to allow Congress to work on a solution for the long-term unemployed, who have seen their support vanish.

The benefits, which apply to people who are unemployed for longer than six months, were left to expire on Saturday after a bipartisan budget deal on federal spending for the next two years failed to include a reauthorisation of the program.

In a clear sign that Democrats plan to make poverty and inequality major issues in this year’s Congressional mid-term elections, Harry Reid, the Senate majority leader, told a reporter in his home state of Nevada earlier this week that the bill will be put to a vote when the Senate reconvenes on Monday.

A senior Democratic aide involved in the legislation said any vote may now be pushed back to Tuesday or Wednesday, to make room for the Senate’s confirmation of Janet Yellen as the chair of the Federal Reserve. But the bill remains a priority.

“We have a commitment that the the unemployment insurance bill be one of the first things the Senate moves on,” the aide said. “This is not some abstract political issue. If Congress doesn’t do this, and do it quickly, people will be choosing whether to pay rent or be out on the streets.”

On Thursday, the Labour Department reported that 1.39m people received the special extended benefits during the week ending 14 December, under an extension enacted in 2008, at the start of the recession, in order to help people looking for work.

Last month the Labor Department announced the US unemployment rate had hit a five-year low of 7% in November, but long-term unemployment remains stubbornly high. In November, some 4.1m people had been jobless for 27 weeks or more, unchanged from the previous month. Those individuals accounted for 37.3% of the unemployed. The expiration of the Emergency Unemployment Compensation (EUC) program on 28 December means that only one one in four unemployed Americans are estimated to receive jobless benefits — the smallest proportion in half a century.

Democrats believe the issue could lose Republicans votes in this November’s midterm elections. Some of the highest rates of unemployment are in Republican-controlled states, and polls show the public supports reintroducing federal benefits for the long-term unemployed.

President Barack Obama is expected to make tackling economic inequality a major priority for 2014 and his administration has thrown its weight behind the Senate push to reintroduce the benefits program. Gene Sperling, the director of the White House’s National Economic Council, said on Wednesday the president was committed to providing support to the long-term unemployed – a move administration economists say would also boost the wider economy.

“Failing to extend emergency unemployment insurance through 2014 will negatively impact 14 million Americans – the 4.9 million workers who will see unemployment insurance cut off and the approximately 9 million additional family members they are supporting,” Sperling said. “But if Congress does the right thing and acts to extend emergency unemployment benefits through 2014, it is estimated to lead to 200,000 jobs and a fifth of a point of additional economic growth.”

The bill extending the program for three months – which would be applied retroactively, reimbursing those who lost benefits over the last week – is authored by senators from the two states with the highest unemployment rates: Jack Reed, a Democrat from Rhode Island, and Dean Heller, a Republican from Nevada.

In his brief remarks about the bill, Reid told the Associated Press he was hopeful the bill would pass in the Senate, but was unsure if it would succeed in the Republican-controlled House. “I don't predict anything in the House," he said.

In the House, Democratic representative Sander Levin, the ranking member of the House ways and means committee, is working closely with the party’s whip, Steny Hoyer. However, congressional analysts believe the bill is unlikely to succeed without support from senior Republicans in the House, which has so far been absent.

The Congressional Budget Office estimated on Tuesday that the Heller-Reed bill would cost £6.4bn. Around 1.3 million jobless Americans received their last payment on Saturday. On average, a further 72,000 Americans are projected to lose their unemployment insurance each week through the first half of the year.

However, as unemployment is expected to decline, the cost of the program will decline through the year.

A recent study by the liberal Economic Policy Institute said that while it would cost roughly $25.2bn to continue the extensions, the economic stimulus would be significantly amplified because of the “multiplier” effect.

That is principally because research shows the long-term unemployed are likely to spend most if not all of their benefits on basic necessities, such as food and rent, thus boosting the economy.

Economist Heidi Shierholz, who jointly authored the study, said on Thursday that paying out unemployment insurance is consistently ranked as the second-most effective economic stimulus available to federal policy makers, after spending on food stamps.

“There is a consensus among the people who look at the data that a major problem in the economy right now is weak demand,” she said. “Those unemployment benefits were going straight back into the wider economy, increasing demand, and as of 28 December that has all been been sucked out. The one thing I can say is the decision to allow these insurance benefits to expire cannot be based on economics.”