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House Minority Leader John A. Boehner, Ohio Republican, sought to counter that image during a meeting with Republican members Wednesday morning, saying that they “have a responsibility to tell the country” that Mr. Obama’s $3.6 trillion budget is “a bad budget.”

Signaling that Republicans are ready to take on Mr. Obama more directly after avoiding head-on criticism for much of his first five weeks, Mr. Boehner said, “There’s no point in triangulation.”