If the Supreme Court has primary or direct jurisdiction, they would have decided this sticky issue long ago. It must be brought to them as an appeal from a lower court.
Article III, section 2, of the Constitution distributes the federal judicial power between the Supreme Court's appellate and original jurisdiction, providing that the Supreme Court shall have original jurisdiction in "all cases affecting ambassadors, other public ministers and consuls," and in cases to which a state is a party. In the Judiciary Act of 1789, Congress made the Supreme Court's original jurisdiction exclusive in suits between two or more states, between a state and a foreign government, and in suits against ambassadors and other public ministers. The Supreme Court's jurisdiction over the remainder of suits to which a state was a party was to be concurrent, presumably with state courts since the statute did not expressly confer these cases upon the inferior federal courts.
The vast majority of the Supreme Court's cases in which it has had original jurisdiction have been suits between the states, but those have been a relatively small part of that case load.