Privatising the government is a bad idea. We at least pretend that the government exists at the consent of the people, and as such, we allow it to tax us. If the government were to be privatized, we'd be allowing corporations to directly take money from our paychecks.
A better idea would be to take the government out of business. Any corporations that exist for pretty much the sole purpose of military production should be nationalized, beyond that, the government should divest itself from any business concerns. No more business welfare, no more doing anything that requires interaction with the corporate world. Boil the government down to three key areas. National defense, Internal security, Justice. Within those areas, things like disease control and national transportation networks can be rationalized, but there's no need for the government to be funding insanity like corporate welfare.