When the gov't provides a service like Medicare to someone, the dollars transferred to Americans has nothing to do with what wages Medicare employees are paid. Administrative costs include everything from IT infrastructure to property leases to paper. None of that has anything to do with wages.
Well for one, you're making a weird assumption here, that all the federal employees in the U.S. account for a significant % of the employment and that if they were
all taken away, that it would have a very adverse impact on the unemployment numbers. Except I'm pretty sure everyone here sees that federal employees need to exist in large #'s, with that definition varying widely. So the only contention is how many should exist, and
that number is what's quite small.
For example, there are currently over
~ 155M people in the workforce, a total of
~ 19.5M government employees in the entire country, and only
less than 3M of which are federal employees. Those 3M gov't employees are less than 2% of the total workforce, and the $14T in debt is a federal deficit that obviously isn't the same as state or local debt (and very little of which actually goes to states).
Your assumptions about how much wages account for of GDP make general sense but honestly I wasn't able to google any good results or find any BLS info on it. Even if it were 2/3rds wages, a certain % of those 66% (of $14T) of federal gov't wages would still necessarily exist in the first place as I said in the previous paragraph, meaning a sizable chunk of your 3%-4% number of federal employees (call it 3.5%) would exist regardless of a handful of "wasted" trillions because it means next to nothing to an economy that has accumulated a couple hundred trillion over the past 30 years, $14T of which was debt. There's simply no way you can claim that accounted for any terribly significant impact on the unemployment rate. Bottom line, you're probably talking less than 1% of jobs impacted by part of that $14T in debt.
It isn't though, as my numbers just showed. Federal employees will always exist, so just because we spend too much for a few years doesn't suddenly mean that had any significant impact on the unemployment rate over the past 30 years. The numbers don't add up to what you think they do.