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On Wednesday, and again on Friday, Mr. Boehner said he would be willing to accept a deal to avert the looming tax increases and spending cuts if that deal cleaned up the tax code — which he said would produce a stronger economy and therefore more revenue to the government. Fellow Republicans said that, too, should have been discussed within the House Republican Conference first.

Asked whether he would be able to sell any revenue deal to Republicans, Mr. Boehner was confident.

“When the president and I have been able to come to an agreement, there’s been no problem getting it passed here in the House,” he said.