Without the safety valve of a democracy all the ideologies are going to be fighting for a piece of the power. Communism or Socialism would gain a large boost in popularity, especially in the urban north. Populism and Fascism would rise mostly in the south. The army would probably mostly support Fascist movements, as loyalty to the removed democratic government would make allying with the capitalists unpalatable, and the general right leaning would make an alliance with socialists unpopular too.
Hoover and the FBI would probably strike out on their own...
Minorities, especially in the south would lean more towards the left, even more so with the South contesting for power. Anarcho-Capitalists would get the support of the mob and mafia, and definitely would have the cash-on-hand advantage.
It'd be like the infighting in Europe during the Interbellum and the reprisals after the war. Japan would take advantage of the situation and scrap the Washington treaty. Might even see if they can seize the Philippians while we're distracted.
With Europe divided between the three ideologies, there's very little they could do to stop the fighting and would likely fan the flames.
No matter how it turns out though, America would be extremely isolationist afterwards. The war in Europe would go along without American intervention, and America would be unable to enforce an oil embargo against Japan.