Untrue. If government employees didn't do their jobs, the entire economy would collapse into chaos, and there wouldn't be any tax revenue at all.
Arguments like yours only work if you imagine the government's contribution of law and order and public service being provided by acts of God, or benevolent fairies or something.
The government could contact those jobs out and get all the same work done for less money
First of all, untrue. Look at anything where third party companies are involved compared to direct government employees, and you'll find it always costs more, all due to the profit taken by the private company. That's why student loans have been taken away from the banks as middlemen.
Secondly, irrelevant even if it was true; it would still be the government spending resources to get a result, and your argument, if valid, would hold true either way. It doesn't, therefore it's NOT valid.