I don't think the chances are too good. Although some states, such as Virginia or New York, could probably make it on their own, many of the smaller states certainly couldn't. Even more, this is an era where many independent nations threw up tariffs against one another and so, it would make sense for the smaller American states to group together into larger nations. I could definitely see a New England Confederation, an independent Virginia and New York, and then a Southern Confederation form. As to how that would come about, I'm not sure.
Possibly a New England exists (Nexit?) during the War of 1812 and the US get solidly beaten. The rest of the US begins to fragment after the loss as the individual states begin to look out for their own regional interests over the good the entire nation?