On the Senate floor, McConnell, R-Ky., said every senator could spend time discussing the perfect solution, "but the end result would have been the largest tax increase in American history," Politico reported.
"The president wanted tax increases, but thanks to this imperfect agreement, 99 percent of my constituents won't be hit by those hikes," he said. "So it took an imperfect solution to prevent our constituents from very real financial pain. But in my view, it was worth the effort."
Democratic Sens. Michael Bennet of Colorado, Tom Carper of Delaware and Tom Harkin of Iowa voted against the bill, as did Republicans Chuck Grassley of Iowa, Mike Lee of Utah, Rand Paul of Kentucky, Marco Rubio of Florida and Richard Shelby of Alabama.
Absent and not voting were Sens. Jim DeMint, R-S.C., Mark Kirk, R-Ill., and Frank Lautenberg, D-N.J.
"This historic vote protects working families from an income tax increase and spares our economy from a devastating political disaster," Sen. Dick Durbin, D-Ill., assistant majority leader said. "We now turn to the House and ask them to act with dispatch to prove our government can truly respond in a bipartisan way in the best interests of the people we represent."
The House Rules Committee already waived the 3-day review requirement, setting the stage for a New Year's Day vote. But The Hill said it was unclear if the House would take up the bill before Thursday, when the 113th Congress will be sworn in.
"The House will honor its commitment to consider the Senate agreement if it is passed," Boehner said. "Decisions about whether the House will seek to accept or promptly amend the measure will not be made until House members -- and the American people -- have been able to review the legislation."
"I don't see any balance yet, that's the fundamental problem," Rep. Jason Chaffetz, R-Utah, told The Hill. "If you don't cut spending, there's no way you're going to pick up Republican votes."
House Democratic Leader Nancy Pelosi was non-committal publicly but signed off the deal in private, a source familiar with discussions told The Hill.
"I understand at the present time, Senate Democrats are meeting with the vice president," Pelosi said in a statement. "When a final agreement is reached and passed by the Senate, I will present it to the House Democratic Caucus."
The bill also would:
-- Extend by five years the college tuition tax credit, the child tax credit and the earned income tax credit.
-- Set the capital gains and dividends tax rate at 20 percent, up from 15 percent.
-- Reinstate the Clinton-era limit on itemized deductions for individuals earning more than $250,000 and families earning more than $300,000.
-- Permanently patch the Alternative Minimum Tax and extend a number of expiring business and energy tax provisions for a year.
-- Freeze scheduled cuts to doctors' Medicare payments for one year, paying for them with spending cuts in other healthcare spending
-- Extend by a year the 2008 farm bill without dairy reforms.
"There is a feeling ... that it's not that this proposal is regarded as great or is loved, in any way, but it's a lot better than going over the cliff," Sen. Charles Schumer, D-N.Y., said.
Conservative and liberal advocacy groups and unions both blasted the bill, The Hill said.
"To be clear, this is a tax increase," Heritage Action for America, a conservative advocacy group, said in a statement while urging lawmakers to oppose the deal.
Liberal groups and unions complained the White House and Democrats were ceding too much, particularly given that Obama pledged during the campaign to raise tax rates on households with annual income of more than $250,000.
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