“If the joint select committee does not do what it needs to do,” said Representative K. Michael Conaway, a Texas Republican on the House Armed Services Committee, “most of us will move heaven and earth to find an alternative that prevents a sequester from happening.”

After listening to dire predictions by the Joint Chiefs of Staff about the effects of automatic cuts, Representative John Garamendi, Democrat of California, was even more blunt. “The sequester will never take place,” he said. “It’s not going to happen.”

Senator Jon Kyl of Arizona, the No. 2 Republican in the Senate and a member of the deficit-reduction panel, has repeatedly said he has no intention of letting such cuts occur. Some House members said they were being urged by military contractors and others in their districts to avert such reductions.

Representative Chris Van Hollen, Democrat of Maryland and a member of the panel, said the attempt to undo the triggers “reflects a total lack of seriousness.” Adding that such efforts would not be successful, he said they were “the result of people trying to escape the fundamental choices before us, and one of those choices is whether or not we are willing to end special interest tax breaks to pay for defense.” The White House is also highly unlikely to approve such actions. The president is averse to the military cuts, but saw the threat of them as a way to pressure Republicans to reach a deal. “There is more fear this time,” Representative Mo Brooks, Republican of Alabama, said about the anxiety being expressed by military contractors in his district. Mr. Brooks said he voted against the debt-ceiling legislation because of the possibility of deep Pentagon cuts.

Under the debt-ceiling budget agreement, members of the joint committee, evenly divided between the parties, have until Nov. 23 to recommend ways to reduce budget deficits by at least $1.2 trillion over 10 years. Both houses are supposed to vote on the package by Dec. 23. If no legislation is enacted, the government would automatically cut almost $500 billion from military spending, with an equal amount from nonmilitary programs, between 2013 and 2021.