I think it would be more like the Russian Civil War—Red and White armies battling for the nation.
In both the Russian and American Civil Wars people were much more independent in terms of how they obtained food & fuel; those two items make any large-scale violence very unlikely and easy to suppress. Even the LA riots, as small as they were, had law enforcement concede the streets to the animals, who promptly went home when the mail (and welfare checks) weren’t delivered.