Not disagreeing with the main premise, but the situation is somewhat different if the rebels obtain military equipment and know how to use it.
If the Air Force SAC base command defects for example in Minot. That is the concern in a civil war. Will nuclear weapons be used to defend the Republic?

Aside from this possibility there is always irregular partisan warfare, harassing and intimidating murders of military officers or political leaders or family members by well armed civilians. While not a win for the old Republic exactly, it would doubtlessly be quite satisfying for the teenager carrying the gun to kill an enemy general.

Overall however, this is an absurdity since there is no rallying point-back to the Constitution will not work, power to the States might work but then the problem of governance arises once more. People are fairly incapable most of the time, so reconstituting a polity during wartime brings a host of problems the Founding Fathers and Honest Abe never faced.