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The Senate bill extends unemployment benefits, full Medicare physician payments and the payroll-tax cut for two months, and also includes language forcing Mr. Obama to make a decision on building the Keystone XL pipeline that would bring oil from Canada’s tar sands into the U.S. The added that spending and lost revenue is offset by a new fee on mortgages.

That measure passed by a 89-10 vote, with seven Republicans, two Democrats and one independent opposing it.

The House bill extends all of the same provisions for a whole year, and forces a decision on the pipeline. It offsets the cost by rewriting parts of the president’s health care law and freezing federal workers’ salaries.

The House bill passed by a 234-193 vote, with 10 Democrats in favor. Fourteen Republicans joined 179 Democrats in opposing it.

The Senate deal materialized after Democrats dropped demands for a tax increase on millionaires. Senate Republicans also support the proposal because it forces the president to give an up-or-down ruling on the proposed Keystone oil pipeline.

The White House put off a final decision on the environmentally sensitive $7 billion project until after next year’s election, but the president has left room to negotiate.

White House communications director Dan Pfeiffer, in a statement Sunday, said they want the short-term payroll-tax extension now to provide assurances in the near term.

“As the president said yesterday, it is inexcusable to do anything less than extend this tax cut for the entire year, and Congress must work on a one-year deal. But they should pass the two-month extension now to avoid a devastating tax hike from hitting the middle class in just 13 days,” Mr. Pfeiffer said. “It’s time House Republicans stop playing politics and get the job done for the American people.”

Mr. Boehner said much of what Mr. Obama has requested previously is in the Republicans’ House version of the bill.

“I think if you look at the House-passed bill, we did everything the president asked for,” he said. “We paid for this, offset it with reasonable reductions in spending. Ninety percent of those reductions, frankly, the president agrees with.”