I also want to say that I think there is a vast gulf between "liberty" as an ideological term, and "liberty" as in a condition of being that actually exists in the real world, has an impact on your behaviour, etc.
For instance, I could live in some sort of libertarian autocracy, where decisions are made by land-owners, and people have only certain negative rights, and no positive rights. I would have more "ideological" liberty, in that I could contract freely, I could do whatever I wanted to the land I have legal title to, etc. But in terms of actual, real-life liberty, such a system would most certainly result in less liberty. You would be more free in one sense (you can do certain things otherwise not possible in a social democracy), but drastically less free in another sense (the average person would absolutely struggle to maintain a good quality of life, as wealth and power would be concentrated into big landowners, the legal system would be privatized, etc).
All of which points to the idea that more government = less liberty is not axiomatic, but is instead an ideological argument that attempts to ignore the externalizations of a particular ideology.