It would look nothing like the original American Civil War; this would be a 4th generational war. The most conventional it would look like would be the war against the Iraqi insurgency. Defections and sabotage within the US military combined with attacks on infrastructure would reduce its ability to function normally.

In such a scenario, Humpty Dumpty is not being put back together again. The US would most likely break apart, assuming some foreign power doesn't manage to conquer all of its former territory.