Simple reply: Long term, not by much.
Complex reply: The CSA would inevitably collapse because of its very nature, without a war holding it together, its "confederation of states" would quickly collapse to secession. And, the USA would slowly reabsorb these, with a warhawk-like party taking advantage of the situation. Of course, racism would take a while to die down, but overall in the grand scheme of things, the continent would stay much the same.
Complex reply: The CSA would inevitably collapse because of its very nature, without a war holding it together, its "confederation of states" would quickly collapse to secession. And, the USA would slowly reabsorb these, with a warhawk-like party taking advantage of the situation. Of course, racism would take a while to die down, but overall in the grand scheme of things, the continent would stay much the same.