An idea toyed with occasionally here is the idea of an independent New York, which a few vague independence movements sprang up in around the time of the Civil War.
Let's say New York is able to get independence - presumably just the city, and that for one reason or another (perhaps an alliance with another nation mixed with a Confederate victory) it survives.
Assuming the stars align correctly, could it survive?
Resources are scarce and I'm not sure how willing other countries would be to do trade with it.