Here's a challenge, and I'm also interested to know what effects this may have on things. Have Alf Landon beat FDR in the 1936 Elections, and then explain what effects you think this may or may not have on future events.
Al Smith (Or an alternate Democrat) manages to beat Hoover in 1928. Delay the Depression or in some other way get Smith to limp to reelection 1932. Franklin Roosevelt wins the nomination in 1936 and is crushed by Alf Landon running on a progressive platform. This may cause the Republicans to end up on the left and the Democrats on the right of the political spectrum thanks to no New Deal coalition.
Two problems though; How does Al Smith win once, never mind twice, and would Landon still be the candidate if the Republicans are largely guaranteed victory in 1936?
Well, you can have Hoover get closer to the Democrats in the years immediately after the war; in OTL he, like Eisenhower after him, was largely a man without a party who was courted by boy parties. He runs in 28 as a Democrat with Smith as him running mate, and narrowly defeats the Republican candidate. The Depression occures on cue, and Alf Landon emerges as a darkhorse candidate for the Republicans in 1932, winning an overwhelming victory in the general, and winning reelection in1936.
I think given the right number of factors Landon could conceivably beat FDR.
Let's take for our POD Huey Long surviving his assassination attempt in 1935. He gains a bit of popularity and decides to begin pursuing his presidential ambitions. In 1936 he launches a primary challenge against Roosevelt forcing the President to defend his record to maintain his hold on the nomination. Never one to play clean, Long secretly arranges to have FDR's condition revealed in a very public manner. FDR stumbles and falls during a campaign speech and suffers a nasty gash to his forehead. Though FDR is able to recover and win the Democratic nomination, Long gains a surprising amount of support and breaks with the Democrats to form the Share our Wealth Party.
Long later announces his intentions not to run in the election under the Share our Wealth banner but his acolytes such as Father Coughlin opt to run in his place. Long quickly endorses Coughlin and campaigns as part of the Share our Wealth party. FDR and the Democrats are forced on the defensive and swing a bit further to the left in order to prevent the SoW party from grabbing too many votes.
Meanwhile Alf Landon runs a strong campaign that attacks both the Democrats and the extremism of the Share our Wealth party. Come election Day Landon manages to take advantage of the divide in the popular vote to come up the middle and win the election by a hair.
Thoughts?