But Republican Senate Minority Leader Mitch McConnell said that "in order to achieve something around here, you have to compromise".
The deal thrusts the contentious Keystone XL pipeline, to carry oil from Canada's tar sands to the US Gulf Coast, back onto the political agenda.
Obama had put off a decision on the project, which pits environmentalists against labour unions and business interests in his political base, until after the November 2012 elections in which he is hoping to secure a second term. The move drew Republican howls.
Instead, the bill gives him just 60 days to review the pipeline project, a deadline Obama did not mention during his brief remarks.
"This bill will stop President Obama's delaying tactics," said Republican Senator Richard Lugar.
"It is absolutely incredible that President Obama wants to delay a decision until after the 2012 elections apparently in fear of offending a part of his political base."
The White House's apparent concession in agreeing to legislative language requiring Obama to ostensibly reconsider it within two months will enrage environmentalists, who lean Democratic and campaigned against the project.
Republican Senator Kay Bailey Hutchison acknowledged "stark" differences between the parties over how to pay for the tax-cut extension, with some MPs on both sides of the aisle furious that the bill slashes inputs to the already-creaky social security system.
"We don't think that we should defund social security," Republican Senator Mark Kirk said alongside his Democratic colleague Joe Manchin. Both had voted against the measure.
The House of Representatives, which earlier approved the spending bill, could take up the tax cut measure on Monday, capping a frenetic period of manoeuvring between the White House and its Republican foes.
Amid the bitter sniping between the two major parties, Representative Debbie Wasserman Schultz said her fellow Democrats in the House would back the payroll tax cut bill but that the pipeline amendment was a mistake by her rivals.
The Republicans had "probably killed the Keystone pipeline" by forcing the Obama administration into a review of two months rather than one year, she said.
Democratic Senate Majority leader Harry Reid said Americans "should know that we fought hard to make sure that they get their checks, and their deductions come January 1".
But Republicans crowed that they had forced Obama to take up the pipeline project, which they say will create 20,000 jobs, even after the president said he would reject any attempt to link it to the payroll tax holiday.
The agreement requires the State Department to issue a permit for the Keystone project within 60 days unless Obama certifies that it is not in America's national interest.
Such a finding would expose Obama to politically explosive Republican charges that he rejected the creation of 20,000 jobs at a time of high unemployment and in the middle of an election year.
Seeking to stimulate the sluggish recovery, Obama had asked Congress to extend a payroll tax holiday for a year to give workers a US$1,500 tax cut next year.
Obama's Democratic allies had initially hoped to fund the project by imposing a tax on the country's wealthiest people, those who earn more than US$1 million a year.
But they met stiff opposition from Republicans, who control the House, and had to abandon the plan.
-AAP