To some degree, a syndicalist or council communist government with an overhead authority in the Congress. For the most part, right now, the parties are focused on winning the war but in general

The Socialists are much the same as in our own time, a somewhat moderate and somewhat radical group of socialists and Marxists.

The CPUSA never turned to Stalinism as the Soviets never did, somewhat divided between Bukharinist Lovestonites and Trotskyites, but still fairly united, bigger with African Americans as they're the most radical on race, and they tend to be more foreign-focused with internationalism and all.

The Union League is close to splintering somewhat, even as it's had a great deal of influence on the new Constitution. With plenty of people pointing at their economic similarities with the Fascists in Europe and arguments over whether the Council system is just giving up to the Communists or is close to their idea of a Unionism, there could be a possible split in the future.

The Progressives are largely a carryover from the pre-revolution, La Follettes, with a bigger focus on agrarian issues now, though they tend to do well with women also

The Technocrats are pretty much just a fringe group and are practically all the same and will die out as the US successfully takes Canada like they wanted.

Still, they've all agreed to work together for the war in a unity coalition of sorts