In a timeline where the USSR didn't collapse and the Cold War escalated into a full-blown nuclear conflict sometime around the year 2100, the world is left utterly devastated.
Both the Soviet Union (and its satellites) and the NATO nations are wiped off the face of the earth, leaving only pockets of survivors scattered around the world.
It's basically your run-of-the-mill post-apocalyptic scenario, except it just so happens that one place, in particular, was spared (the specifics as of why are too long to discuss, let's say it just happened).
Civilization still remains in a small state in the US, where life goes on. It's nothing like pre-war life, but there's still a somewhat functioning government presiding over various scattered communities, all working together as the state that once was...
Now, with all the backstory out of the way, I'll get to the meat of the question:
Assuming there had been preparations for the eventuality of nuclear war (and that by sheer luck no hits were taken in its territory), could such a state have survived in isolation? If so, which US state would realistically be the most qualified for post-apocalyptic self-sufficiency?
EDIT: Just for clarification, this isn't about the conditions necessary for the scenario (there's plot armor for that don't worry), but rather about the possibility for such state to still survive (even if barely) after being cut off the rest of the world, and which state could be a good candidate for that.
Also, I should have pointed out that in this future scenario most of the world is heavily relying on renewable energy sources, so the absence of fossil fuels isn't a real issue anymore, as solar panels and wind farms are the norm.
Still, thanks for all the feedback!