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Mr. Obama’s own defense secretary warned those cuts would be devastating to the military, and some lawmakers on Capitol Hill have said they will try to pass legislation to undo them.

“My message to them is simple: No. I will veto any effort to get rid of those automatic spending cuts to domestic and defense spending. There will be no easy off-ramps on this one,” the president said.

He said the only bill he will accept to head off defense cuts must find cuts elsewhere, or raise taxes.

The failure of the supercommittee and the $15 trillion national debt have been easy targets for Republicans on the campaign trail, where some of them, including Mr. Romney, have vowed to block tax increases and cuts to defense, which makes up about 20 percent of federal spending.