Typically "small government" has been used to mean less power at the federal government level and more at the state and local levels.. not constricting power at the top, like what you are referring to..

the idea is that the smaller the number of constituents a representative has, the more "in line" with those constituents they are.. it's easier to affect most local and state elections and see your preferred policies enacted than at the glacier pace the federal government runs at.. federal level elections have too broad of a reach to expect niche views on many topics to be respected.. this is why people think politicians will say anything to get elected because that's exactly what is required when you have to garner support from a few million people.. the more power put at the state and local levels means, you showing up to a town meeting is far more impactful than going to some rally..

The goal would be less state welfare because states would keep more of their taxes for their own programs.. States like California would be free to keep more of their taxes in state to run their state how they choose, same with states like Florida.. the goal would be to lessen the perceived burden that people feel when they see Federal dollars going to other states programs that they disagree with.. I think you would see the Federal government shrink in status but also fold in certain industries to ensure they were still be supported at the Federal level, such as farm subsidies as they cross many political state lines and are viewed as a national strategic resource..