operate without enough oversight
This is your opinion. FISA Court exists for a reason, and is there to protect the rights of Americans.
frequently flaunt the law (and ignore the constitution)
No idea how you're getting to this assumption, unless you're taking clickbait at face value. There have been contested judgements regarding the legal justification for metadata collection. That hardly constitutes "ignoring the constitution." I'm also curious as to your claim of frequency.
eroding the rights of the people they're supposedly serving
NSA cannot collect information about American citizens, only FBI can. I believe NSA can only be involved with a specific warrant issued in response to an imminent or direct threat, but even then, I think it has to be FBI.
The military is completely different
This is the point I'm trying to make to you: NSA is the military. One more time. NSA is the military. Excuse the gross oversimplification, but NSA provides intelligence to other branches of the military so that they can function in the most informed way possible.
If you "can't possibly fault the soldiers" who are "on the ground" and "generally following orders," I'm going to assume that you are someone that supports keeping US soldiers as safe as possible. Yet, you seem to delight in the notion that the NSA would be shut down for a week, which would directly endanger those lives. How would you rectify this?