Assuming a Great Depression, then the only vaguely plausible scenario I can think of is an earlier Huey Long or Huey Long-type* insurgent running on a third party ticket and throwing the election to a non-Hoover GOP candidate.
This isn't so ridiculous when you consider FDR ran as a pretty traditional candidate in '32--'36 is when he's a firebrand campaigning against the established order.
(*LaFollete won 16% in 1924--you need someone to repeat that in this election.)