But I'm thinking on a grander scale. What if all 50 states and various islands and territories up and left at once? Or at least tried to? Granted, some people have formed their own country without any borders, and I fully support their efforts, but actually taking real estate away from a country is a surefire way to get their attention (cf the Civil War).
You could still have good trade relations with the former United States (if any), and negotiate free border crossing and so forth. But you'd be freed from having your citizens drafted for silly wars you don't support, federal income tax (if you liked), bizarre laws, global scorn, and silly internet/phone regulations and tariffs.
I'd suggest you be good to any native peoples within your borders, have reasonable rules governing internet commerce, maintain nice highways, keep national parks (but now they're your national parks), and advocate small government (town meetings are good) and limits on what developers can do to your land, people, and tax base (Vermont's Act 250 is a good model).
1Sources: Out: The Vermont Secession Book, Mares, Bill;
The Vermont Manifesto: The Second Vermont Republic, Naylor, Thomas H.
2I'm flying there on Thursday.