It seems that there are more than a few independence movements going on in the USA. One of them I know of in my own area (the Pacific Northwest), is called the Republic of Cascadia (combining the states of Washington and Oregon), and it’s NOT one of those neo-facist/neo-nazi ideas of a separate nation.
How many new nations would be carved-out of the USA if these independence movements achieved their goals of breaking-away from the USA?
It could be a large number, depending on how broadly you define a movement. You also run into some problems because some of the territories would overlap (for example, the Southern secessionists would incorporate Texas, infuriating the Republic of Texas folks).
Besides the southerners and Texans, I also know of The Conch Republic in the Florida Keys.