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A senior Democratic Senate aide said that “all options should be on the table.”

The payroll-tax cuts have been overshadowed by the fight over the fate of the George W. Bush-era tax cuts that also expire in January.

Mr. Obama and most Democrats want to extend them only for individuals making less than $200,000 and couples earning less than $250,000, while Republicans want to continue the cuts for everyone.

This story was based in part on wire service reports.