The US Military is a constitutional endeavor of the US. Of course, it's government run. Conservatives don't want all government gone, those would be anarchists (i.e. Occupy Wall Street types), but want government to be efficient, constitutional, and not trying to control or tell people how to live their lives (i.e. limiting sizes of soft drinks in NY or requiring the purchase of health care). Nice strawmen you constructed of conservatives/Republicans, but as with Obama's strawmen, totally false.