The House Republican leader, John A. Boehner, on Sunday opened the door to a compromise on the contentious issue of the Bush-era tax cuts, saying he would vote to maintain lower rates for families earning less than $250,000 even if President Obama and Democrats insisted on ending the cuts for wealthier Americans.

With Congress returning to Washington this week, Mr. Boehner's decision is likely to reframe both the final intense weeks on Capitol Hill before the elections and the fall campaign, in which embattled Democrats have planned to paint Republicans as obstructionists favoring the rich over the middle class.

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