Immediately after talking to reporters, Obama left the White House to fly back to Hawaii, resuming the vacation he suspended after Christmas to return to the capital for budget talks.
In the Congress, Republicans vowed to press on in the weeks ahead to cut spending in ways they could not in the fiscal cliff deal.
"Now the focus turns to spending," House Speaker John Boehner, R-Ohio, said in a statement after the vote. "The American people re-elected a Republican majority in the House, and we will use it in 2013 to hold the president accountable for the 'balanced' approach he promised, meaning significant spending cuts and reforms to the entitlement programs that are driving our country deeper and deeper into debt."
Reluctant House Republicans, concerned the plan had too few spending cuts and not enough meaningful debt reduction, had threatened to stymie the plan. Their fury was fueled further by a new report from the nonpartisan Congressional Budget Office that the package would add $3.97 trillion to deficits over the next decade.
But they also came to realize that scuttling the package could instantly put the nation's slowly improving economy in jeopardy. Tax rates had already gone up Tuesday, and automatic spending cuts were scheduled to kick in Wednesday.
In private meetings Tuesday, Republicans expressed concern that once domestic financial markets re-open after the New Year's Day holiday Wednesday, reaction to legislative gridlock could be severe. It's a risk, said Rep. John Fleming, R-La., "we all recognize."
As a result, the debate became a virtual celebration of bipartisan agreement. "After more than a decade of criticizing these tax cuts, Democrats are finally joining Republicans in making these tax cuts permanent," said House Ways and Means Committee Chairman Dave Camp, R-Mich. House Democratic Leader Nancy Pelosi, D-Calif., lauded the bill as a "very, very strong first step as we go into the new year."
The legislation, passed by the Senate 89 to 8 Tuesday morning, will postpone the automatic spending cuts for two months. Individuals making more than $400,000 - $450,000 for families - would pay a top income tax rate of 39.6 percent, up from the current 35 percent. Others would pay at 2012 rates.
The plan also ties the alternative minimum tax to inflation, a relief for an estimated 30 million taxpayers who could have been hit with higher bills. Other measures include an extension of jobless benefits for the long-term unemployed and avoiding a huge cut in Medicare payments to doctors for a year.
The vote in the House came after a day of furious closed-door lobbying - and arm-twisting. Vice President Joe Biden met for two hours with House Democrats. At the same time, Republicans met privately twice, for a total of nearly three hours. They heard opposition from Majority Leader Eric Cantor, R-Va., who has a strong following among conservatives. "There was a lot of discontent in that room," said Rep. Steven LaTourette, R-Ohio.
The congressional turmoil was no surprise. Republicans have long been unhappy with Democrats' reluctance to agree to big spending cuts, and were not pleased the latest deal delayed the automatic cuts.
"This does nothing about getting the $16.4 trillion debt under control, said Rep. Steve Chabot, R-Ohio.
Republicans made a last-ditch effort to pass more spending cuts, offering to consider the same package of $328 billion in cuts that passed on a party-line vote Dec. 20, but could not muster enough support Tuesday. Many Republicans worried that attaching the measure would never make it through the Senate, putting the entire fiscal cliff deal at risk.
"We don't want to do anything in the House that would create a poison pill for the Senate," said Rep. Raul Labrador, R-Idaho.
Few lawmakers in either party seemed happy with the plan, as the unease Tuesday crossed party and ideological lines.
"This punts the problem," said Rep. Raul Grijalva, D-Ariz. "It just sets us up for more fights."
But few dissenters spoke during the debate. Rep. James Moran, D-Va., said the bill will "set up three more fiscal cliffs," including fights over raising the debt ceiling and the sequester and said "and all that's left is the spending cuts. What programs do we cut and how deep? We're going to look back on this night and regret it."
House Republicans were not pleased that they had virtually no input into the deal, crafted by Biden and Senate Republican Leader Mitch McConnell of Kentucky.
LaTourette called the plan "a package by a bunch of sleep-deprived octogenarians."
The loudest protests came from the 87 Republican freshmen first elected in 2010, swept into office on a pledge to drastically slash federal spending.
"There is a resignation that the big steps forward my class wanted to take is not possible with this Congress," said Rep. Rob Woodall, R-Ga. "Only small steps forward are absolutely possible."
Whether he and others could accept such small steps was the key to approving the deal. Veteran Republicans argued the package was as good as they were going to get.
"Let's recognize we avoided what could have been a terrible outcome," said Rep. Tom Cole, R-Okla.
He urged resisting changes. "It's too late in the game," he said. "You can keep tinkering with this, but you're not going to make it perfect."
Economy still likely to take a hit
Lawmakers managed to avoid driving the United States over the so-called fiscal cliff with a late-night vote Tuesday. But higher taxes and brinksmanship in Washington are likely to sap strength from the fragile economy well into 2013.
The law will raise taxes on individual incomes over $400,000 and household incomes over $450,000, on investment profits and dividends, and on the portion of estates that exceeds $5 million. Those higher taxes on the wealthy are likely slow the economy a little bit.
But a bigger drag on the economy will come from a tax hike Democrats and Republicans didn't even bothering to fight over: the end of a two-year Social Security tax cut.
The so-called payroll tax is scheduled to bounce back up to 6.2 percent this year from 4.2 percent in 2011 and 2012, amounting to a $1,000 tax increase for someone earning $50,000 a year.
Mark Zandi, chief economist at Moody's Analytics, calculates that the higher payroll tax will reduce economic growth by 0.6 percentage points in 2013.
The Associated Press