You keep on and on with the limited government thing as if that is the key to liberal/conservatism. But the size of government is not a core value of either liberal or conservatism. The fact that conservatives harp today on small government is a passing thing, a campaign gimmick, as it was at one time when the liberals demaded small government. Generally the party out of power wants a small powerless administration, but of more import to each, is the type of govenment, which side the governnment supports that is important.
Actually, there's a little more to it than that. Agrarian liberalism is different from industrial liberalism. Agrarian liberals do want a very limited central government, not as a core value, but as a means to an end.
Liberalism is ALWAYS about equality, and hence about liberty. Or vice-versa: liberty, and therefore equality. Because it's gross inequality that is the main threat to liberty; when one person is vastly more powerful than another person, he is able to impose his will on the weaker person and compel obedience. But exactly how that mechanic operates, and therefore what to do about it, is different in an agrarian economy than in an industrial one.
In an agrarian economy, a strong central government can and usually does enforce the privilege of the landed elite: very wealthy owners of large amounts of good land, who work that land by means of forced labor (usually slavery but sometimes a kind of bonded peasantry or serfdom instead). Liberals oppose it for that reason. Also, agrarian liberals feared the rise of a capitalist industrial economy and the elevation of a super-wealthy commercial elite, which a strong central government could facilitate through central banking, high tariffs, and subsidies.
Thomas Jefferson, James Madison, etc. opposed a strong central government but only as a means to an end, not as an end in itself. Classical liberals were quite willing to use government force where it served the ends of equality and liberty.
Industrial liberalism seeks the same things as classical liberalism -- liberty and equality -- but does so by different means because it occupies different circumstances. On land, you walk; in the water, you swim; both are done for the purpose of moving. In an industrial economy, a strong central government is unavoidable and the only question is whether it serves the interests of the commercial/capitalist elite or those of the people as a whole.
Neither modern liberals nor conservatives oppose "big government," but neither do they advocate it as an end in itself.
As always, the ends of liberals are liberty and equality, and so liberals advocate government activities that serve these ends while opposing government activities that oppose them.