Provided it is staffed with real relevant experts -- efficiency experts, forensic accountants -- and has no power beyond making reports and recommendations to Congress.
You want to create another govt dept with no actual power to do anything, staffed with a bunch of high paid eggheads to send recommendations to Congress where nothing gets done because Congress has no interest in making govt smaller. Sounds perfect.
Have it run by vetted retired volunteers. No money just reimbursement for travel expenses, etc. That way you get people who know how various systems work and will put a value on things that affect most citizens like Universal Health Care and Social Security. Then they can come up with some real consequences when, for example right now the Defense Department has failed what, the 7th annual audit in a row? You misfile your taxes 7 years in a row and I guarantee they're going to be chatting with you about what consequences you are looking at.