But House GOP leaders signaled that they would not hold votes on a deal until Tuesday, meaning the United States will go over the "cliff" at least for a few hours.
In remarks designed to raise pressure on lawmakers, Obama said cutting healthcare costs must be a priority in any future package to reduce the deficit.
"I’m willing to reduce our government’s Medicare bills by finding new ways to reduce the cost of healthcare in this country," Obama said.
"That's something that we all should agree on. We want to make sure that Medicare is there for future generations. But the current trajectory of health care costs is going up so high we've got to find ways to make sure that it’s sustainable."
He added that any reforms must be accompanied by changes to the tax code to prevent "wealthy individuals, the biggest corporations" from using more loopholes and deductions than the average person.
Medicare is a major driver of the national debt, and its costs will rise as the U.S. population ages over the next several decades.
Republicans have proposed converting the program to a premium-support system — something Democrats decry as a massive cut in seniors' benefits.
Read more about the possible "cliff" deal here.