Eh. I get what you mean that it's unclear this envisioned "small government" actually looks like, but it is relatively clear how Republican voters define the success or non-success of Republican economic policy. Success in the eyes of a Republican voter means having more disposable income. And whatever "small government" means, it's clear that the Republican theory about slashing government is primarily a matter of means, rather than ends: that is, slashing government services, lowering taxes and deregulation are, in theory, the means of generating more wealth for the middle-class.
Less important than how small government "makes you feel" is the argument that government bureaucracies are insulated from free market competition, and therefore they don't provide services as cheaply or as efficiently as they would if they were exposed to competition, so they should be privatized. Less government means more services that people rely on are made more efficient by competition, and so less government is better than more. At least, that's the argument.
Obviously, it seems dubious that the theory has any connection at all to reality. Does Republican economic policy actually promote economic growth? Whether it does or not, Republican supporters can still find themselves getting wealthier during Republican presidencies and attribute it to the policies of their government. But, of course, when the personal wealth of middle-class Republican voters diminishes, they become dissatisfied and don't turn out to the polls.