People forget that the Republican Party was pretty leftist in a lot of respects back in those days. In New York, people like Nelson Rockefeller and John Lindsey were high-profile Republicans who weren’t conservative in any sense of the term.
The DemoPublican Party pretty much gave in to the ideas of the fascists (national socialists) in the 1930s - the welfare state, a planned economy, trade unionism and the use of the mass media and arts to propagandize for the state. It took von Hayek, Mises, Freidman and a number of others to create the intellectual basis for a return to sanity and classical liberalism (and I use this term very precisely) which form the core of modern conservative philosophy.