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But Republicans’ support for smaller government is a basic party principle, and GOP leaders and champions of cutting government waste could have a tough time rejecting the president’s proposal outright.

A spokesman for House Speaker John A. Boehner said he hoped the plan would be more than just window dressing.

John Hart, a spokesman for Sen. Tom Coburn, Oklahoma Republican, who has spent years fighting for leaner, more efficient government, called Mr. Obama’s proposal a small step in the right direction.

“[Sen.] Coburn applauds the effort and believes that Congress needs to go much further,” the spokesman said.