If there's one thing Americans would bring on a deserted island, I know for a fact it would be a jar of dill pickles. First of all, pickle juice is said to be hydrating and restore electrolytes, so it would be great for hot days on the island. Secondly, they would make a tasty food source.
Lastly, they're just great, and there is no denying that dill pickles are a treasure for the American people.