So there were a few loonies running around North America in this period, but generally nothing on Europe, where they were actually able to come to power. Gaining control of a country in fractious, war-torn Eastern, Central or Southern Europe is generally going to be easier thain gaining control of a country with the geographical size, population and wealth of America. So to give the extremists a fighting chance, the challenge is for the Great Depression to be bad enough that it leads to coups, civil war and fragmentation. Bonus points for two or more of the following groups gaining control over a piece of the country:
Smedley Butler and the Bonus Army
Huey Long, Father Coughlin and the Share Our Wealth Party
American Legion and the Business Plotters
Howard Scott and Technocracy Inc
Jack Reed and the Combined Syndicates of America
Charles Lindbergh and America First
William Simmons and the KKK
Neo-Confederates
Fritz Kuhn and the German American Bund
MacArthur and a junta of national preservation
anything else you can think of...
Edit: POD is post-1900 obviously.