You have to keep in mind that the Democratic party in the 30’s and 40’s is not the same Democratic party as today. Likewise, the Republican party of the 30’s and 40’s is not the same party that exists today.
The GOP especially was in turmoil during the 1930’s. You had some like Landon who ran against FDR in 1936 who agreed with FDR more often than not. He didn’t offer the voters much of a choice. Then you had two other prominent factions fighting for control of the GOP, neither of which resonated with the people: The pro-Germany wing, and the strict isolationist wing which sometimes allied itself politically with the German sympathizers.
Given all that, FDR couldn’t help but win.
Honestly, it doesn’t sound too much different than what’s going on today. The Republican party is divided into tow factions: the conservatives, or the Tea Party, and the liberal RINOs, known as the establishment Repubs. Alf Landon was obviously a RINO. Kind of reminds me of McCain during the campaign saying that we didn’t have anything to fear from Obama.