There are large economic, political, and cultural divides in the US (at least more so than other countries). Some states actually have economies that are competitive at a global scale (i.e. California, Texas).
For these reasons, it would be really interesting to see a balkanized US. Assume the best for this scenario. The new nations adapt quickly to form independently functioning economies. You can address this question by discussing one new hypothetical country or all of them. What would their form of government look like? What would their foreign policy look like? What would be their main source of revenue? Would there be animosity between countries? What would their trade relations look like?