Oh, certainly! But I can personally give you examples where government could be greatly more efficient with Six Sigma (Department of Agriculture, for example). Heck, anywhere there is scientific testing of any sort is a golden opportunity!
See also: Infrastructure
You have to add 'honest' to the adjectives for testing. I really doubt whether you'd get any non-engineering government agency to honestly test themselves. The primary self-test for government agencies is $$ spent, the more the better. And that's not something Newt is going to be able to change.
The problem isn't to get government really efficient in what it currently does, but to greatly reduce what it does and to be some what efficient in the reduced work load.