Those tax increases — plus $109 billion in defense and domestic spending cuts that were to be automatically triggered Wednesday — became known as the fiscal cliff. Economists warned that their combined impact would hurl the economy back into recession, but Obama's signature on the bill would prevent the "cliff" from taking hold.
Obama can sign the bill remotely using a machine called an "autopen," or the bill can be flown to Hawaii for his signature.
Overall, the legislation would add nearly $4 trillion to federal deficits over the next decade compared with what would have happened had all the tax cuts expired, according to the nonpartisan Congressional Budget Office.
"I'm embarrassed for this generation. Future generations deserve better," complained one foe, Rep. Louie Gohmert, R-Texas.
The agreement's journey to passage was a tortured one. It included negotiations between Obama and Boehner on a larger, deficit-cutting deal that collapsed, and a failed effort by the speaker to drum up enough GOP votes to pass a "Plan B" that would have limited tax boosts to incomes exceeding $1 million.
It took weekend talks between McConnell and Biden, former Senate colleagues, to craft the more modest package that focused on averting the worst impacts of the fiscal cliff while postponing any deficit reduction efforts to coming months.
Those first showdowns will come over the next three months, when the government's legal ability to borrow money will expire and temporary financing for federal agency budgets will expire. Republicans have already said that, as they did in 2011, they will demand spending cuts as a condition for extending the debt ceiling.
"Now the focus turns to spending" and overhauling the tax code, Boehner said in a written statement after the vote. He said the GOP will fight for "significant spending cuts and reforms to the entitlement programs that are driving our country deeper and deeper into debt," a reference to costly benefit programs like Medicare, Social Security and Medicaid.
Spending cuts are "going to be a component of every single battle we have" in the new Congress, conservative GOP Rep. Marsha Blackburn of Tennessee told CNN on Wednesday.
Obama, in his White House remarks, said that while he was open to compromise, he would demand deficit-cutting savings from added revenue on the well-off, not just spending cuts.
He also pointedly said he would "not have another debate with this Congress" over extending the federal borrowing limit.
"If Congress refuses to give the United States government the ability to pay these bills on time, the consequences for the entire global economy would be catastrophic — far worse than the impact of a fiscal cliff," he said.
Though its focus was on taxes, the measure approved Tuesday would prevent a potential doubling of milk prices and prevent a $900 salary increase for members of Congress in March. Its extension of jobless benefits would help 2 million people out of work at least six months, and it would prevent a 27 percent cut in reimbursements doctors get for treating Medicare patients.
Weighing in with criticism of the compromise were the chief authors of an influential bipartisan deficit-cutting proposal, former GOP Sen. Alan Simpson and Democrat Erskine Bowles, a former White House chief of staff under President Bill Clinton. They called the measure "truly a missed opportunity to do something big to reduce our long term fiscal problems."
AP reporters David Espo, Charles Babington, Andrew Taylor and Larry Margasak contributed to this report.