The measure by Udall, a Democrat, and Sen. Jon Kyl, R-Ariz., was added to the Senate's defense authorization bill Tuesday.
It would create an advisory panel to recommend ways to reform the National Nuclear Security Administration.
In a joint statement, Udall and Kyl said they sponsored proposal "in light of major management issues, cost overruns and security breaches in recent years."
"The NNSA has been plagued with problems that have impacted the scientific and stockpile stewardship work being done at Sandia and Los Alamos National Laboratories, as well as the security and safety of the workers there," he said in a joint statement with co-sponsor Sen. Jon Kyl, R-Ariz. "The ineffectiveness of the NNSA is a serious national security issue and our amendment will take a good look at what is needed to reform it."
Nuclear watchdogs, however, criticized it as an attempt to give for members of Congress the power to seat a panel that will make recommendations to protect the private contractors that run the nation's nuclear facilities.
Greg Mello, executive director of the Los Alamos Study Group, said the proposal ignores advice from government auditors to absorb NNSA back into the Department of Energy, aiming instead "toward freeing the powerful nuclear contractors, whose management has recently produced a string of multi-billion-dollar cost overruns and failures, from the limited accountability they now have."
The proposal is not part of the House authorization bill and would have to be added in conference committee negotiations to become law.
Approval of the amendment came the same day the NNSA and the contractor that runs Los Alamos announced the contractor would pay $10 million for cost overruns on a faulty $213 million security system.
The money will cover "potentially unallowable costs" incurred in construction of the system, which was built around what is known as Technical Area 55, the only place in the country where nuclear weapon triggers can be made.
Officials have estimated it will take an additional $41 million and another six months to fix the system, which was supposed to be up and running this summer.