Updated

The Senate on Saturday approved a two-month extension of the payroll tax cut, teeing up another partisan fight early next year over President Obama's favored tax break as well as a separate battle over a controversial pipeline.

The bill, however, is not a sure thing in the House, where rank-and-file Republicans gave leadership an earful Saturday afternoon. The House had earlier approved a yearlong extension, and many members were disappointed by the Senate's decision to pass a short-term fix.

One source on the Republicans conference call Saturday told Fox News there was "overwhelming opposition."

"Never heard words like 'sucks' and 'crap' (in a conference call)," a House Republican added. "Almost all on the call sounded angry."

House Speaker John Boehner is trying to convince his caucus to consider as a victory the inclusion of a provision meant to speed up the so-called Keystone pipeline. The House is set to come back into session and vote on the bill Monday. If House GOP leaders cannot muster a bipartisan majority to pass the Senate bill, they could either push to amend the package or try to force the Senate to accept the House-passed bill from earlier -- one Senate Democratic Leader Harry Reid described as dead on arrival.

On the Senate side, lawmakers decided on a two-month extension after they were unable to agree on how to pay for a package that would extend the tax cut through the next election. Democrats originally wanted to use a millionaire surtax to finance the measure but abandoned the call in the face of deepening gridlock on Capitol Hill. The $33 billion two-month package instead uses fee hikes on new mortgages backed by Fannie Mae and Freddie Mac.

Final passage would mean American families would continue to enjoy a 2 percentage point cut from their Social Security tax. In addition, weekly jobless payments averaging about $300 for millions of people who have been out of work for six months or more would be continued. The measure also provides a 60-day reprieve from a scheduled 27 percent cut in the fees paid to doctors who treat Medicare patients.

The Senate voted 89-10 in support of the package. Later in the morning, the Senate also passed a $1 trillion budget bill. The 67-32 Senate vote, which followed passage in the House, ensures the funding of 10 Cabinet departments as well as military operations in Iraq and Afghanistan, and averts a government shutdown.

Obama, in a brief statement Saturday afternoon, said he expects Congress to extend the payroll tax cut again -- preferably financed by a tax on wealthy Americans -- in two months.

"It is my expectation that it would be inexcusable for Congress not to further extend this middle-class tax cut for the rest of the year," he said. "It should be a formality."

Democrats hope to use the pressure of an election year to fight for the extension.

But the bill also puts some election-year pressure on Obama. To the administration's chagrin, Republicans were able to secure in the legislation a provision that compels Obama to make a decision on the fate of the Canada-to-Texas Keystone pipeline in 60 days. The administration had earlier delayed the project until after the election over environmental and safety concerns, though unions support it and the project could create thousands of jobs.

While administration officials have suggested the GOP pipeline provision could imperil the project, Republicans are hoping that Obama will ultimately clear the way for the pipeline to proceed.

"Here's the single largest shovel-ready project in America," Senate Republican Leader Mitch McConnell said on the floor Saturday. "It is literally ready to go with the permission of the president of the United States."

The legislation is a partial victory at best for Obama, who's being forced to accept Republican demands for the swift decision on the pipeline and a scaled-back version of his payroll tax cut plan.

In a statement, White House communications director Dan Pfeiffer indicated Obama would sign the payroll tax cut measure, saying it had met his test of "preventing a tax increase on 160 million hardworking Americans" and avoiding damage to the economy recovery.

The statement made no mention of the pipeline. One senior administration official said the president would almost certainly refuse to grant a permit. The official was not authorized to speak publicly.

The developments came a few hours after the White House publicly backed away from Obama's threat to veto any bill that linked the payroll tax cut extension with a Republican demand for a speedy decision on the 1,700-mile Keystone XL oil pipeline proposed from Canada to Texas Gulf Coast refineries.

Fox News' Chad Pergram and The Associated Press contributed to this report.