The passage by the Senate sets the stage for a final showdown in the House, which is expected to reconvene sometime Tuesday or maybe Wednesday.
The last-minute agreement was negotiated between Vice President Joe Biden and Senate Minority Leader Mitch McConnell.
"I can report that we've reached an agreement on the all the tax issues," said McConnell in an afternoon speech on the Senate floor. "We are very, very close."
A potential mini-deal would raise taxes for families making over $450,000. That's higher than the president's goal of $250,000. It would increase the estate tax, or the so-called death tax from 35 to 40 percent, and it would extend unemployment benefits for some two million people for one year.
"For the last few days, leaders in both parties have been working toward an agreement that will prevent a middle class tax hike from hitting 98 percent of all Americans starting tomorrow," the president said. "Preventing that tax hike has been my top priority because the last things folks can afford right now is to pay an extra $2,000 in taxes next year. Middle class families can't afford it, businesses can't afford it, our economy can't afford it.
The main sticking point centers on federal spending cuts, like the more than $1 trillion of automatic cuts to defense and domestic programs that is set to begin Tuesday.
Congress could pass later legislation retroactively blocking the tax hikes and spending cuts.
Several Democrats also voiced disappointment with the president and emerging deal.
"This is one Democrat that doesn't agree with that at all," Iowa Democratic Sen. Tom Harkin said of the tentative deal. "No deal is better than a bad deal, and this looks like a very bad deal, the way this is shaping up."
ABC News and The Associated Press contributed to this report.