Even American conservatives haven't actually been in favor of small government for a very, very long time. Roughly 40 to 50 years as a majority position (some of them still lie and pretend they are of course; they always flake when it comes to actions & votes).

George W. Bush nearly doubled Federal Government spending and built numerous massive new bureaucracy agencies. Reagan before him did likewise in regards to spending. They're almost all big government conservatives now, the only question is what they spend on.

There few conservatives in the US holding the political position of cutting government spending, and almost none in favor of cutting entitlements. The tiny wing of the Republican party that actually favors the free market heavily, is irrelevant and has zero power or influence.