They wouldn't last long enough to elect a President. This isn't 1850 where nobody relied on electricity, running water, and USD . If the CSA tried to secede again, their state economies would go belly up within seconds and the international community would not recognize them. There wouldn't even need to be a war.
You're right. The US relies on fossil fuels and Texas is #1 in crude production, natural gas production, and electricity production. We have our own electricity interconnection and electricity reliability council.
The US would have plenty of coal left, though.
So you're saying free trade isn't necessary?
Most any state would flounder economically very shortly after leaving, and any state that did not would inevitably be bombed and droned into submission. Sizable segments (in most cases, majorities) of the armed forces in these states would not side with their state National Guards and governments, making defense practically impossible (though doing so would be difficult, anyway; read my first sentence). The United States would almost certainly embargo the entities in question, and presumably, practically any other country would refuse to engage economically with them for fear of angering us.
Presumably (like with the Texas example given by AD), the US would first attempt to secure resources and production hubs critical to the national economy in these states at the onset, and attempt to defend them. I imagine it would be easier to do with assets along the coast or off-land. Individuals attempting to "liberate" these facilities from the US would likely be shot, bombed, etc, in the name of national defense. If defense and procurement of these sites became impossible, then I could definitely see a Kuwait-style response in which Texas' power plants, refineries et al are bombed so as to be of no use to anyone. This might also be the first time in which we see mass deployment of EMP technology.
With acute political polarization (as alluded to with the armed forces scenario), one and/or the other of the following would occur: civil war of its own would break out within the seceding territories, and a mass exodus of "non-believers" to more stable areas of the US would occur, causing further economic damage to the areas in question. Practically any and all national/multi-national companies and corporations would close their doors in the affected territory at least temporarily, if not permanently, sealing their fate.
