A full blown civil war is completely out of the question, but a civil uprising or insurgency is definitely a potential.
Depends on whether it's the left or the right uprising. The Left? Pretty unlikely as they're way too easy to starve out, too separated, and lack a common belief/motivation. The only moderately large places where they have sizable amounts of support are the West Coast, New York and the Tri-State Area, and the Black Belt, which are all pretty isolated, and bar the Black Belt, dependent on imports from producing regions to maintain their populations. I also doubt the citizens of the Black Belt would want to fight for a Communist/Socialist uprising, if that was the case. That, and a centre-left person just lacks the motivation overall to rise up, especially against a government like the US. If it was a monarchy or a theocracy, maybe, but not a moderately conservative democracy - A Communist and a Socialist might, but not a Liberal or a Progressive.
A Conservative uprising though? They'd probably do pretty well. Lots of them have access to firearms, their sizable support is in rural, producing regions that makes them much harder to starve out, and since the place is rural, it'd be incredibly difficult to fully destroy them without salting the earth, and no country wants to take such drastic measure and end up ruling a pile of worthless dirt with a pissed-off populace. If the success of insurgencies in Afghanistan is anything to go by, they'd be hard to weed out. And although they also lack a common belief/motivation, an ultranationalist and a conservative would be more likely to work together than a Communist and a progressive. Granted, a Conservative doesn't really have much of a motivation to rise up right now, but going after their guns would probably be enough to push them over the edge.
Granted, there's always the joke that the Government would just roll out tanks/jets/helicopters to destroy any insurgency, but you can't really do that against your own citizens, except in the rare case that they've formed a sizable ground army of their own, which is unlikely. Most of your citizens, regardless of their opinion of the insurgency, wouldn't be happy seeing the US army kill it's own citizens and level it's own settlements. And if you think that the US would even THINK about using nuclear weapons on it's own territory, you're absolutely exceptional.
So overall, a full blown civil war ain't happening any time soon, and it's still pretty unlikely that we'll see a civil insurgency either, but if we end up getting a right-wing insurgency, it has pretty good odds to succeed. A left-wing insurgency has much worse odds due to how easy their major support areas would be to starve out.