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For defense, Mr. Jordan said it “has to be on the table.” Beyond waste, fraud and abuse, he said, the best place for cuts might be to look at civilian employees within the Defense Department. He said he has heard that idea from folks in the department.

Even then, he wouldn’t commit to any specific cuts. Instead, he said he supports giving the department a once-over to see what might be possible.

Mr. Jordan voted against last year’s debt deal that set up the sequesters, but now says he would oppose any effort to turn them off unless they are replaced with other spending cuts.

Mr. Jordan also said he agrees with some of his party’s leaders who think that the GOP is playing offense and could even expand its majority in the lower chamber.

That puts him at odds with House Minority Leader Nancy Pelosi, California Democrat, who told reporters last week that she is increasingly convinced her party will regain control of the chamber, particularly now that Rep. Paul Ryan, a Republican Study Committee member and architect of the GOP budget with its Medicare changes, is on the presidential ticket.

“Since the selection of Ryan and his being the agent for the destruction of Medicare, that has changed things much more to our favor, and other, shall we say, indiscretions, whether it’s the Sea of Galilee or statements by Congressman Akin,” she said, referring to two other recent controversial incidents.

The first involved a Republican congressman who went skinny-dipping on a trip to Israel, and the second was a reference to Rep. W. Todd Akin of Missouri, a Senate candidate who said women’s bodies have a way of rejecting pregnancies when they are victims of “legitimate rape.”

Mrs. Pelosi said Democrats will win 12 or 13 seats across California, Illinois, Texas and New York, and win a seat or two each in Maryland, Washington and Arizona based on redistricting. Then in Florida, Colorado, Ohio and Nevada, she said, her candidates can ride Mr. Obama’s coattails to victories that will give Democrats the 218 seats total needed to control the chamber — and maybe significantly more should Mr. Obama win in a landslide.