There are also bans based on animals being in the wrong places (no natural predators), or because they are nuisances (certain farm animals in areas zoned residential).
New York City I believed banned Ferrets.
A majority of states have at least some bans on ownership of exotic or non-native animals. From an article about a group pushing Governor Strickland to ban ownership of bears: "Ohio is one of 20 states that has no law prohibiting private ownership of dangerous, non-native animals. It is one of the top two states for exotic animals sales and auctions."
Here's a site I haven't verified that lists exotic animal bans and restrictions in the United States. If the list is correct, it does appear that many states DO ban the ownership of tigers, although certainly not all.
I think it is clear that there are many laws in many states that already restrict the ownership of pets, including banning different types of animals. Banning pit bulls would not be something "new" for most localities, just an application of legal jurisprudence they already have employed.
BTW, I can say clearly that I oppose a federal ban on pit bulls. The federal government has no business telling people what they can own. This is a state/local issue, and each state/locality needs to make their own decision.
I absolutely agree that the federal government should have nothing to do with it. If a ban happens at the local level, at least the owners have options.