"We've got to do what it takes to protect the middle class, grow this economy, and move our country forward," Obama said in his weekly radio and Internet address.
"Leaders in Congress are working on a way to prevent this tax hike on the middle class, and I believe we may be able to reach an agreement that can pass both houses in time," he added.
The comments came after Obama met with top congressional leaders Friday and said that Senate Democrats and Republicans would work overtime this weekend to try to head off a $500 billion time bomb of tax hikes and spending cuts, dubbed the "fiscal cliff", before a January 1 deadline.
The president, sensing a mandate from his re-election last month, wants to raise taxes on the rich but exempt the middle class. Republicans want only to close tax loopholes to raise revenue and demand significant spending cuts in return.
But if nothing is done by the deadline, all taxpayers will see an increase.
Following the White House talks, Democratic Senate Majority Leader Harry Reid and Republican Minority Leader Mitch McConnell will now head efforts to seek a deal before Tuesday.
But any agreement would also have to pass the House of Representatives, where there is doubt that any deal signed off by the Democratic president would win favor with restive conservatives in the Republican caucus.
According to The Washington Post, the deal a "stripped-down" version of earlier proposals dealing mainly with taxes was already within reach.
Citing unnamed people briefed on the talks, the newspaper said it would protect nearly 30 million taxpayers from paying the minimum tax for the first time and maintain unemployment benefits for two million people.
The plan also would halt a steep cut in Medicare reimbursements for doctors and preserve popular tax breaks for both businesses and individuals, such as those for research and college tuition, the report said.
But The Post said the two sides were still at odds over where to set the limits of wealthy at $250,000 a year or $400,000 a year -- and over taxes on inherited estates.
Nor was there agreement on spending cuts so dear to Republicans, the paper said. Hence a deal will not include either them or an agreement to raise the debt ceiling, setting up another fierce battle over the government's borrowing limit in the next two months, according to The Post.
Obama warned, however, that if an agreement was not reached in time, he would then ask the Senate to hold an up-or-down vote on a basic package that protects the middle class from an income tax hike, extends vital unemployment insurance for Americans looking for a job, and, as he put it, "lays the groundwork for future progress on more economic growth and deficit reduction."
He did not elaborate.
"I believe such a proposal could pass both houses with bipartisan majorities as long as these leaders allow it to come to a vote," the president said. "If they still want to vote no, and let this tax hike hit the middle class, that's their prerogative but they should let everyone vote."
Meanwhile, in a weekly Republican address, US Senator Roy Blunt of Missouri, vice chairman of the Senate's Republican Conference, expressed some optimism Saturday, saying he believed that "going over the fiscal cliff is avoidable."
But he severely criticized the Democrats' plan to focus mainly on taxes while setting aside the issue of government spending, arguing that inaction on spending "shouldn't be an option".
"The president's proposal to raise taxes on the top two percent of Americans won't even pay one-third of the annual interest that's now owed on this massive $16 trillion debt," Blunt said. "In fact, the president's tax hike would only fund the government for eight days. Americans deserve to know: What does the president propose we do for the other 357 days of the year?"