What if the President himself is one of the plotters of the secessionist movement and gives them access codes and issues executive orders to the military to help the rebels commandeer nuclear weapons and such?
This way, you're turning people loyal to the president into people helping the plotters, perhaps even unknowingly.
Extremely unlikely, I know, but a still another avenue of possibility to consider...
That's akin to cutting your limbs off and feeding them to the wolves. No President of the US is going to willingly give up part of his country. Any rebel sleeper who might have gotten into office under such ridiculous odds could easily be sucked into power madness and say, "hey! I'm now president of all 50 states of the USA. Why should I listen to some fuck who wants to chip off my domain!?"