This possibility begins and ends with "dead girl or live boy".
The only way I could see it happening is if you get Huey Long running a Southern Populist campaign that goes for a more extreme version of the New Deal along with some punitive anti-business measures that ends up getting support of the Southern states, along with FDR running afoul of the machines in the North that will turn on him if he cranks up an anti-corruption operation, and some kind of measure taken by FDR that runs afoul of the West. And then maybe New England goes back to the GOP with a more credible campaign- nope, can't do it. 1936 was over from the start, and Landon running as FDR-lite is a tried and true tactic of failure.
Nominate someone other than Landon, or have FDR govern as the fiscal conservative that he ran as in 1932, which would prompt a Progressive Party candidate perhaps take Wisconsin and another few states, along with Huey Long take a good part of the south and perhaps even throw Tennessee to the GOP, and have the GOP brand recover under a better candidate than Landon and take New England and the Plains States and- nope, again, you don't get to 270 that way, and the Democrats will have the House.
I don't think this is doable.