Republican and Democratic Senate leaders were tasked to come up with a deal over the next 24 hours.
Earlier, Republican Senate minority leader Mitch McConnell said he was "hopeful and optimistic" that a deal could be reached with Democratic Senate majority leader Harry Reid.
Reid said that any deal would be "imperfect" but that they both have an obligation to do the best they can.
"I'm modestly optimistic that an agreement can be achieved, nobody's going to get 100 per cent of what they want — but let's make sure that middle class families and the American economy, and in fact the world economy, aren't adversely impacted because people can't do their jobs," Obama told reporters.
But Obama said if Reid and McConnell could not reach a deal, he would urge Reid to bring to the Senate floor a basic package — which would preserve tax cuts for middle-class Americans while extending unemployment insurance and lay the groundwork for more economic growth and deficit reduction — for an up or down vote.
"The hour for immediate action is here — it is now," Obama said. "We're now at the point where in just four days, every American's tax rates are scheduled to go up by law."
"Every American's paycheque will get considerably smaller, and that would be the wrong thing to do."
The fiscal cliff is widely predicted to slow, if not kill, any hope of economic recovery in 2013.
Economic measures scheduled to take effect on Tuesday, the first day of the new year, would cut paycheques for most Americans — hence consumer spending — and force the end to an estimated 1,000 government programs. It's those changes that are being called the fiscal cliff, a term coined by Federal Reserve chairman Ben Bernanke.
The net effect has been variously estimated to be equal to a devastating three to four per cent drop in gross domestic product for 2013. And while the country's top lawmakers claimed to be open to a last-minute deal, no one seemed optimistic.
The focus Friday was on the Senate, where Democrats have control, rather than the Republican-led House of Representatives, where an attempt by Speaker John Boehner to create a compromise has already foundered in embarrassment for the Republican leader.
Adding pressure is this week's warning from Treasury Secretary Timothy Geithner that the government would hit its $16.4-trillion borrowing limit on Monday, the final day of the year. That would make it harder for the U.S. to pay its bills.
He also indicated, however, some accounting measures would be available to the Treasury to stave off immediate disaster on the borrowing front.
Canada wouldn't be unscathed
Although the sun would rise after Tuesday's New Year's holiday, with Americans working and spending as usual, a slide back into recession could begin.
Canada wouldn't escape unscathed if the president and Congress fail to reach a solution. Some 76 per cent of Canada's exports go to the U.S., so manufacturers and other exporters would feel any slowdown in demand from the U.S. economy.
As TD Bank economist Craig Alexander told CBC News recently: "It would wipe out economic growth in Canada."
Republicans and Democrats said privately that any agreement would likely include an extension of middle-class tax cuts that had been set to expire at the end of the year, with increased tax rates at upper incomes — a priority that was central to Obama's re-election campaign.
A deal also would likely put off the scheduled spending cuts and extend expiring unemployment benefits, officials said.