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“I appreciate the fact they gave up on their millionaire surtax, but they didn’t give anything up, because they never had it,” he said.

The payroll tax is 4.2 percent this year, but reverts to its usual 6.2 percent on Jan. 1 without congressional action. Both parties have said they want to extend the tax break another year, but are divided over how to pay for it.

Republicans have proposed paying for the tax break by freezing federal workers’ salaries and slowing parts of the Democrats’ health care law.

Mr. Obama has vowed to veto that bill, saying the salary freeze would cut spending too deeply.

The parties also are at odds with GOP insistence that the payroll-tax bill include a provision to force the White House to make a decision on the Keystone XL pipeline, which would carry oil from western Canada to the U.S. Gulf Coast.

The spending-bill impasse broke when Republicans agreed not to block Mr. Obama’s plan to loosen restrictions on personal trade and travel with Cuba, though Republicans kept in a provision Democrats had denounced that would prevent an Obama administration energy-efficiency rule on light bulbs. Democrats also acceded to a ban on abortion funding by the District of Columbia’s government.