A Republican would almost certainly win in 1932, probably of the small-government conservative faction, but their inability to address the impact of the Great Depression beyond some grumbling about pulling yourself up by the bootstraps would pretty quickly hand power to progressives of some kind. Or, if he had a plan, Hoover himself ironically could have been the alt-Roosevelt. He was a progressive and he did have experience with disaster relief in Belgium and in the US.
This is where I think things would go. The GOP probably (if Al Smith's 1st term) or certainly (if John W. Davis's 2nd term) becomes the more progressive party in this scenario.
