No. That is wrong. All of government is overhead, it's like an operating system that way. Public employees should not be collectively bargain to extract more money from taxpayers. If compensation is so bad in the gov't then the employees can organize to get someone else voted in to turn things around. Furthermore, because so much of what happens in government is subject to public scrutiny (as it should be, it's our money) there's much less space for the government to poorly compensate its employees or treat them like crap.

Edit: did people forget what a great contribution to society police unions have made?