The deal ends weeks of partisan bickering that threatened to return payroll taxes to 2010 levels, end extended unemployment benefits for 2 million out-of-work Americans and reduce Medicare reimbursements to doctors by 27 percent.
"I said last week this should be a formality and that is still the case," Obama said in thanking Congress for approving the measure before recessing for the holidays.
"We have a lot more work to do. This continues to be a make-or-break moment for the middle class."
After making his remarks, Obama was to join his family in Hawaii for the holidays.
The deal, which keeps the payroll tax rate at 4.2 percent, gives Congress two months to work out a deal covering all of 2012.
Senate Majority Leader Harry Reid, D-Nev., immediately appointed Sens. Max Baucus of Montana, Ben Cardin of Maryland, Jack Reed of Rhode Island and Bob Casey of Pennsylvania to help negotiate an extended deal.
"I have talked to each of them. They're going to work expeditiously to come up with a long-term arrangement on the payroll tax, on unemployment, of course, and on the doc fix. I have great confidence in them," Reid said during a press availability.
Reid chastised colleagues for playing partisan games.
"I hope this Congress has had a very good learning experience, especially those who are newer to this body. Everything we do around here does not have to wind up in a fight. That isn't the way things need to be," Reid said.
"People wonder why the approval rating of Congress is so low. I don't wonder. Seems that everything we've done this last year has been a knock-down, drag-out fight. There is no reason to do that."
Since most members already had headed home for the holidays, Congress used a parliamentary maneuver -- unanimous consent -- to approve the extension.
First the Senate and then the House approved the extension, ending, for now, protracted wrangling to keep the payroll tax rate at 4.2 percent instead of returning to its 2010 level of 6.2 percent -- an average difference of $24 a week for 160 million working Americans. The bill also keeps long-term unemployment benefits for some 2 million workers from expiring Jan. 1.
The vote came after House Speaker John Boehner, R-Ohio, agreed Thursday to bring up the temporary extension for a vote in exchange for the Senate agreeing to appoint negotiators to work on the longer deal after the holiday recess.
"I talked to enough members over the last 24 hours who believe that, hey, listen, we don't like this two-month extension, we don't like this reporting problem in the Senate bill," Boehner said Thursday evening. "But if you get this fixed, why not, why not do the right thing for the American people, even though it's not exactly what we want."
Hours earlier Boehner said the right thing was to oppose the two-month deal approved by the Senate 89-10 and instead demand the Senate reopen negotiations over the holidays to create a measure that would last an entire year.
Senate leaders balked at the demand.
"We're fighting to do the right thing," said Boehner, flanked by House Majority Leader Eric Cantor, R-Va., and several House Republicans tapped to remain in Washington to rework the Senate deal.
The House rejected the bipartisan Senate bill on a test vote 229-193 Tuesday, with many freshmen Republicans saying the bill was the kind of half-measure they were elected to thwart.
In addition to extending the payroll tax and unemployment benefits, scheduled cuts in reimbursements to doctors who serve Medicare patients are postponed.
The $33 billion package is funded by increasing fees Fannie Mae and Freddie Mac charge lenders for guaranteeing home loans.
In working out the deal, Senate negotiators agreed to make a technical change to ensure small businesses are protected from new reporting requirements in carrying out the two-month payroll-tax extension.