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Mr. Obama voiced a similar message in his White House news conference Friday. He urged Republicans to make the middle-class tax cuts permanent. He said that extending the cuts to wealthier Americans would cost $700 billion and equates to a $100,000 tax break for “millionaires.”

“That, I think, is a bad idea,” he told reporters.

Austan Goolsbee, making his first appearance on the Sunday talk shows after being named to head the White House Council of Economic Advisers last week, seemed uncertain about Mr. Boehner’s statements.

“If he’s for that, I would be happy,” Mr. Goolsbee said on ABC’s “This Week.” “In the past, we have seen some of these circumstances in which what appears to be the offer of doing this — the sensible thing, in the light of day there was a little bit of a feeling, well, if the president is for it, I’m against it, and then it falls apart.”