Not as much as you'd expect. The American radical left had been severely weakened by the effects of the First Red Scare in the late 1910s. By the 1930s, the left's big leaders like Eugene Debs, Bill Haywood, Mother Jones, Emma Goldman, etc were dead or in exile. The only far-left organisation that was able to ride out the Red Scare and remain reasonably strong was the Communist Party USA, largely because unlike the others it was getting support and resources from Moscow.

However, after the catastrophe of Comintern policy in Germany (where divisions between Communists and Social Democrats undoubtedly played a part in the Nazis' success), Moscow instructed Communist Parties round the world to adopt a 'Popular Front' strategy - forming alliances with centre-left parties supposedly to defend against fascism. This made sense in Europe where fascist movements were quite substantial and a real threat, but it was a dumb policy in the US where the closest thing to a mass fascist movement - the Ku Klux Klan - had practically fallen apart in recent years. However, the CPUSA stuck to it anyway, and obediently backed Roosevelt and the New Deal, and caused relatively little trouble compared to the large unrest of the pre-Red Scare labour movement.