How and when does the USSR win the cold war?
I think that is the important question. The USA wasn't a multi ethnic police state and for my suspension of disbelief you need a convincing POD with a LOT of butterflies to have the USA "loose" the Cold War.
And what exactly is "loosing"? Without a nuclear war I don't see a balkanization of the USA in the 20th century.
So I think we need much deeper information about your hypothetical scenario to answer your question.
In fact, the United States is just a multi-ethnic state. But you are right - ethnic boundaries within the US are blurred, this country is a migrant. Therefore, to destroy the US is not so simple. Most likely two variants.
The first is the copying of the socioeconomic and political system of the winner, and the transition into the sphere of influence. The second is the preservation of independence, but the loss of its sphere of influence, the dissolution of economic and military blocs and the withdrawal into isolation. In the domestic policy, radical changes are inevitable.
The most successful time line for victory is the end of the 60's and the beginning of the 70's. In Portugal and Spain, the last breath is prepared for the fascist regimes. In France and Italy, left-wing radical uprisings began. In the United States began a major economic crisis, which then pereros in stagflation. Better than the moment cann't think of.
To win, the Union needs more democracy and socialism.