The difference between calling a relationship a civil union instead of a marriage can still have implications. For instance, even if the two have the same rights in the US, what happens if you're travelling abroad? Will your relationship be recognized at a foreign hospital if you need to conset to care for your incapacitated spouse? Depends on the local laws, and some countries recognize foreign marriages but not foreign civil unions. What if you move to another country? Will your American relationship be recognized there automatically?
Also, if there's a distinction under the law between same-sex marriage and opposite-sex marriage, even if there's no difference in rights now, the fact that there's a legal distinction between them could make it easier for a difference to be created in future.