The world supply would be the same however virtually all oil would be imported. That creates a North which is more economically vulnerable since virtually all oil is imported. Instability would push the price of oil to never before seen levels. If oil doubles in price (not an unrealistic possibility) then we deal with a crisis of affordability. It's entirely within the realm of possibility that price of oil becomes too expensive to buy in needed quantities. To provide an analogy, if there was food but you could not afford to obtain it, then you starve just the same as if the food doesn't exist at all.
The South would not be as susceptible if they used their own oil. If the new government took the oil on a cost of drilling plus a fee basis, then it's removed from speculation and market price pressures. Low energy costs gives a competitive edge to the south. This doesn't mean that the South won't have it's own problems, but my point isn't about how one side or the other is a clear winner, but rather that the red/blue state paradigm people are citing (red states getting more money than blue) is completely irrelevant, and energy is one factor among many.