Yes, the Supreme Court has original jurisdiction. However, that does not mean the court must exercise its original jurisdiction (and, in practice, the court rarely exercises original jurisdiction). And that’s not even relevant here, since neither party has asked the court to take the case that way. The case has already been heard at the district level. The plaintiffs have asked the Supreme Court to take the case, on appeal, before it is heard at the circuit level. Obama, as a party to the lawsuit, is asking them not to do so. Original jurisdiction has nothing to do with this.
I keep seeing this excuse all over this forum. The Court doesn't have to take any case, I guess, but they certainly should take this one, unless they intend to let ObamaCare be fully implemented before they take it up.