"There are still issues to resolve, but we're hopeful that Congress can get it done," he said at the White House against the backdrop of a group of middle-class Americans who would see their taxes go up if Congress fails to act.
Speaking minutes later, Sen. Mitch McConnell, Republicans' top negotiator, said they have reached agreement on raising taxes on the wealthiest Americans while extending Bush-era tax cuts for the rest. But he said other issues, including how to address the looming spending cuts that make up the other half of the "fiscal cliff," remain unresolved.
With the deadline for tax increases less than 10 hours away, Mr. McConnell said Congress should vote on that part of the package and wait until later to tackle the spending cuts and other pieces.
"Let's take what's been agreed to and get moving," he said.
He has been working to strike a deal with Vice President Joseph R. Biden, and said both sides are working in good faith and are "very, very close."
With only less than half a day left before the deadline, Mr. Obama said he planned on spending his New Year's eve in Washington, D.C., along with most members of Congress and the press corps.
"With this Congress, if there is even one second left before you have to do something, they'll wait until the last second," Mr. Obama said.
"The people who are with me here today — they need our leaders in Congress to succeed," he said. "They need all of us to be focused on them, not on special interests but on families, students, grandmas … folks who are out there working very hard and just need a fair shot."
Even if Mr. Biden and Mr. McConnell can come to an agreement in the next couple of hours, a deal can still be derailed by House Republicans who are opposed to increasing tax rates and also from liberals in the Senate who want to see more high-income households forced to pay higher taxes.
The proposal on the table would increase tax rates on some high-income earners to Clinton-era levels, increase the estate tax rate, extend unemployment benefits and potentially put off the $110 billion in automatic spending cuts called for in the legislation that created the fiscal cliff.
The two sides have agreed that tax rates should be extended for individuals with annual incomes below $400,000 and for family incomes of less than $450,000, GOP sources said.
Sen. Lindsey Graham, South Carolina Republican, said the outlines of the deal are a major victory for Mr. Obama.
"Congratulations on your tax rate increase. You fought hard and won," he said on the Senate floor. But he warned that this was just round one in what's a much longer battle, and said round two is coming up in a couple of months when the Treasury Department once again bumps up against its borrowing limit.
Mr. Graham said he will not vote to give Mr. Obama another debt increase unless the president agrees to changes that reduce Medicare and Social Security spending, including limits on benefits.
"The next time we meet is going to be around the debt ceiling. And the image I want is not a bunch of people behind the president clapping for him, but members of Congress, Republicans and Democrats, clapping for the president," Mr. Graham said.
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