Not always. Not all expenditures cut would impact things as such. We have screws that cost hundreds of dollars that our government pays for. The super expensive toilet seats and hammers... not a myth. It is real.
Those things are not that expensive because they have to be in order to employ people. They are that expensive because they can, because they think it is guaranteed they'll be paid for. They do not have to compete. Many of these screws and such are on military hardware.
So there are places that you can cut that do not have the negative effect you speak of. Plus some of the jobs that we have with people sitting on their ass and watching porn all day working in some bureaucratic position actually cost us more than if they were on welfare. Yes, we really do have that situation.
The problem is raising the debt ceiling makes it so they don't even have to attempt to fix these things. In fact, over time we get just more of them.
Still someone's job it is to build those. Is that one overpaid? Likely. Are Managers and football players overpaid? Sure!
The problems you describe happen when private rewards get doled out because not enough people are involved to make good policy the less costly solution.
"Saving" does not change that, because savings never happen t those private rewards.
A dictator always pays the army first is probably easier to understand ;)