It might work well for some states and be horrible for others.
The Dakotas and Montana, for example, would probably be keen to have some sort of better access to shipping ports - as would somewhere like Kansas and Oklahoma. Some states just don't have much to offer themselves: Rhode Island, for example, is small, but they'd survive. Hawaii and alaska might not notice as much change, though their tax rates would probably go up. Both need to import a great deal of food, for example: Alaska has a vast area to cover with infrastructure. Out West there are water issues. And a lot can go wrong getting what the states need since there wouldn't be the federal government to smooth things over.
Not only that, but travel suddenly becomes an issue. Each state needs a passport and to secure borders or to have something akin to EU-style borders. Things that used to be shipped across the country now would be going international. Some businesses would have to reorganize and add some more layers just to deal with the added regulation differences.
States would have to petition other countries to recognize all the different countries.
And even more large would be trying to divide up the military into the different states. How do you decide who gets an aircraft carrier? Are small states just doomed to be weakish?
The closest I can work out to something resembling 'working' would be to divide into regions instead of states - at least it would solve some of the issues, anyway. The military issue really gets to be a pickle no matter how I look at it, though, and would probably be based more on where existing bases are.