I think this doesnt really add up. Cause as soon as the US would invaded Russia, not only would Russia nuke the invading armies. They would very probably also start nuking command infrastructure. Which might or might not trigger the MADs doctrine.
(And it makes no sense to nuke Russia without first evacuating US cities and advising Americans to make fallout shelters, which would mostly consist of trenches dug into the ground covered by logs or plywood covered by a plastic sheet to keep out the rain covered by 18 inches of dirt.)
Think about it. There would be acts of Congress involved with drumming up and establishing funding and fiscal programs devoted to the task of constructing, or making available to everyone the material to construct these types of shelters. Once it was prioritized as s National Security priority posture, you can bet your sweet rear Moscow would be on the line to Washington/the State Department, and similarly mobilizing their own interests in response to what would be a transparent act of escalation in the abscence of any reasonable explanation. It would also be a clear signal to someone who actually had some intent to initiate or chance a strike that somehow, news of that had leaked to their adversaries as well, even if they vehemently denied any such intent up to zero-day.
You don't just mobilize on that kind of scale, militarily, or civically without sending very clear and obvious signals to other nation states with even a modicum of interest in self-preservation in the face of external threats. Especially in today's highly interconnected world.