Al Smith was the Democratic nominee in 1928 and an early supporter of Roosevelt. However, he became disenchanted with the New Deal and broke with FDR to join the American Liberty League, a coalition of conservative Democrats opposed to Roosevelt's New Deal policies.
The question here is, how possible would it have been for Smith to change parties and run as a Republican, or as an independent, against FDR in 1936 or 1940, and what would his chances have been?