Not necessarily. I know it's often used this way in practice, but this is also partly because people perpetuate the notion that you must be a libertarian to believe in such notions, and that sensible liberals are supposed to be in favor of a large state capable of solving any social problem.
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.
Clearly, the statement was in regards to paying less in taxes, which is what was specifically mentioned. Being suspicious of taxation does not translate to exclusively wanting to pay less in taxes.
What does "shrink the state" mean, then? Are those not part of the state? If only the FBI or other armed wings of the state are meant, why not say that?