Or maybe it's code for "I don't want the kind of totalitarian programs mentioned in the OP".
Well, I think that's not true.
There's certainly room on the ideological spectrum for a kind of "liberal minarchism", for the lack of better term. If you think about it, conventional minarchist right-wing libertarianism is often defined by "state as small as it needs to be protect its citizens from aggression, theft, breach of contract, and fraud". But this formula has two parts, each of which can be adjusted independently.
If you take the second part - the list of goals - and add "..., to provide for a basic standard of living, and to constrain economic inequality within reasonable levels", then you basically have a liberal minarchist credo. With libertarianism, it shares the central idea that state is a necessary evil, and it must be only as big as it needs to be, and no bigger. With mainstream liberalism, it shares the desired goals.
In practice, the difference is how you approach the expansion of government. Mainstream liberals often see any expansion that tries to solve some social problem as good, regardless of how important that problem is, and whether non-government solutions exist. A minarchist approach is to start with the premise that any expansion is unnecessary, and require clear justification, with evidence, as to why it is actually necessary.
Would it result in lower taxes? Probably, but that's not the point. The point is to ensure that the government doesn't become a juggernaut that can be easily repurposed for oppression.