They are various local administrations who split for various reasons - some out of severe political disagreements with Washington D.C. (the ultra-liberal Pacific states), some motivated by their strong national identity (very right-wing Texas), some in an attempt to shield themselves from the chaos surrounding them (the isolationist Mormon theocracy in Utah and Florida, although the latter ended up being dragged into the bloody inter-ethnic quagmire in Georgia and Alabama anyway). Many of them are just as dysfunctional and corrupt as the rest of America - I was inspired by the former USSR of the Nineties, after all.
The actual USSR at that point, however, is more like today's China - formally socialist, but de-facto very state capitalist. It started to move into that direction under Stalin's successor Beria, who crushed political dissent, reunified Germany as a demilitarized neutral state in the late 1950s and finished the Palace of Soviets, among other things. After Beria's death in the mid-70s, his successor Pyotr Masherov accelerated the reforms and presided over the greatest economic boom in decades, but ran into problems with nationalists and other radical dissent, received a vote of no confidence and died in the late 1980s. In 1994, the Union is led by a collective leadership, has the most powerful economy in the world and dominates Europe and the rest of the world (with economic influence and a little bit of world police adventures), but is very corrupt and suffers from wealth inequality and other problems. Furthermore, the economy is dominated by megacorporations (imagine a giant electronics manufacturing conglomerate called Elektronika, for example). The well-off areas like the European part of the USSR and major cities elsewhere are a nice place to live, though.
However, it'll go into the "prelude" part - the setting is urban fantasy/science fantasy, and it is mostly set in 1980s-early 1990s (before shit hit the fan) and 2000s (afterwards, possibly the main part, or maybe not). A lot of things happen:
- Criminals and police in America and Russia suddenly must have to deal with magic-wielding competition from parallel worlds;
- Black supremacists, neo-Confederates and the Federal forces in the war-torn American South suddenly must have to deal with a mind-bending eldritch alien thing from a parallel universe;
- A good part of southern United States and the Caribbean suddenly must have to deal with being wiped out by a giant interdimensional rift;
- The entire world suddenly must have to deal with a devastating alien invasion from a parallel universe (and suspiciously sudden arrival of other aliens wanting to help);
- The invading aliens suddenly must have to deal with a counter-invasion by allied forces;
- The entire world suddenly must have to deal with the aftermath of the whole mess. But hey, there's now a brand new world to colonize! Too bad the alien allies removed all sensitive technologies like FTL because they didn't trust the humans 'enough'.
10 years later, in most of the (former) Northeastern United States, which formed the Federation of New England and which narrowly escaped devastation because of
dumb luck, humans and newcomers from various worlds try to make a living. USSR took the main force of the blow, lost 25-30% of its population and turned into a military dictatorship ruled by some
General Lebed' - it's busy rebuilding itself and colonizing "Terra Nova" with the rest of Europe (also not really democratic these days). The rest of the world, especially Africa and Southeast Asia, remain devastated at best or completely depopulated at worst.