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The supercommittee, born of this past summer’s bitter debt-ceiling deal, is tasked to find by Nov. 23 ways to lower the debt by $1.5 trillion. Failure would trigger $1.2 trillion in automatic spending cuts that would affect a wide range of domestic programs and the Pentagon.

Should the supercommittee fail, there has been speculation some conservatives in Congress would push for legislation to undue the trigger process because it would hit defense and other GOP-favored programs hard.

But former Sen. Pete Domenici, New Mexico Republican, said such a move would be disastrous because it would portray Congress as inept and would suggest to some around the world that the United States is “well on our way to becoming a second-rate power.”

Mr. Simpson had harsh words for outside advocacy groups he said are trying to bully Congress into accepting a debt-reduction plan that isn’t balanced. He accused Grover Norquist, who heads the anti-tax-increase group Americans for Tax Reform, of holding dangerous influence over conservative lawmakers.

“He has people enthralled,” Mr. Simpson said. “That’s a terrible phrase. Lincoln used it. It means your mind has been captured, you’re in bondage with the soul.”

Mr. Simpson also chastised the AARP for running a TV advertisement that warns lawmakers against Medicare cutbacks, calling it “the most disgusting ad I’ve ever seen.”