They're not small government...Just government that agrees with their view on the world.
If they were small government they'd allow people to marry who they please and end the war on drugs.
The bolded is a straw man.
Advocates for "small government" have never said that government should be idle (i.e. "small") in all public policy areas. Mostly, conservatives speak of "small government" in the context of economic matters, such as decreased regulation, fewer entitlements, less spending, and lower taxes. That part of the ideology is implicit in the phrase, "Small government."
In matters of security, on the hand, conservatives believe that government should be active (i.e. big).
Unless you faithfully represent the position of "small government" advocates, then you can't truly have a discussion about "small government" advocates.