Bishop, who represents Utah's major military installations, such as Hill Air Force Base, said he would look for ways of heading off the cuts, which would start at the beginning of 2013. That includes Sen. John McCain's plan to offer legislation to protect the military.
But Bishop won't find much support from his home state colleagues.
"That's classic Washington," said Rep. Jason Chaffetz, R-Utah. "You set up a deal, but don't want to deal with the consequences."
Like Chaffetz, Democratic Rep. Jim Matheson and Republican Sen. Mike Lee say they won't support legislation to stop the budget cuts from moving forward. Sen. Orrin Hatch, the top Republican on the Finance Committee, is remaining mum on the issue for now.
"It is premature for Senator Hatch to get involved when he very well could be in the middle of it moving forward," said Hatch spokesman Matthew Harakal.
The whole situation is an outgrowth of the contentious debt-limit debate from earlier this year. In exchange for allowing the nation to borrow more money, Congress created a supercommittee of six Democrats and six Republicans who had until Thanksgiving to identify $1.2 trillion in savings over the next 10 years.
To give them an adequate incentive to compromise, the deal called for politically unpalatable cuts in the military, Medicare and a whole host of discretionary programs if the supercommittee failed, which it did Monday.
"Although the committee has failed, the cuts are still happening," said Matheson, the only member of Congress from Utah who supported the debt-limit increase. "There will be cuts and that's something I supported in the first place."
He wanted the supercommittee to identify much more than $1.2 trillion in deficit reduction, saying the only way for Congress to balance the budget would be through a bipartisan compromise. But the supercommittee fell victim to the same partisan gridlock that has stopped previous congressional attempts to reduce the debt.
The Democrats want any deal to include a tax increase on the wealthy, while Republicans are opposed to any tax increase. And Republicans want to find big savings through Medicare and Social Security, programs that Democrats are fighting to protect.
Chaffetz said it may take voters in the 2012 election to end the stalemate.
"This country has a stark contrast between the two parties," he said. "This election will be a dynamic one for sure."