Speaking at an event at the White House Tuesday, Obama said the legislation would restore benefits to millions of people who have been struggling to cope with the "aftermath of the worst economic crisis in generations", Xinhua reported.
"So letting unemployment insurance expire for millions of Americans is wrong. Congress should make things right. I am very appreciative that they're are on their way to doing just that," said Obama.
Obama said legislation would restore unemployment benefits to people
"We've got to get this across the finish line without obstruction or delay, and we need the House of Representatives to be able to vote for it as well. And that's the bottom line," he added.
In a 60-37 vote earlier on Tuesday, the Democratic-controlled Senate passed a motion to begin debate on the bill, which would provide a three-month extension of the benefits programme.
An estimated 1.3 million unemployed Americans saw their benefits lapse when the programme expired Dec 28.
The benefits came from the Emergency Unemployment Compensation programme, enacted under the Bush administration in 2008 to provide supplementary relief for the long-term unemployed who have exhausted standard state benefits.
Democrats argued that the extended unemployment benefits provide vital lifeline to the unemployed and critical economic stimulus to the US economy by boosting consumer spending.
According to Republicans, unemployment benefits can be a disincentive for job hunting, and with the jobless rate now at a five-year low of 7 percent, such emergency federal assistance is no longer necessary.
Senate Minority Leader Mitch McConnell said before the vote on Tuesday that his party could accept extending the federal benefits only if they were paid for.
Extending jobless benefits is part of a larger message of economic fairness the White House and Democrats seek to highlight in the new year.