1) Chances are better?
2) Already have one judge, maybe you get more, to stand up for you before going to the Supremes.
3) Gives you a bit more time to craft a petition for cert.
I don't see too many justices getting into this one. Scalia and Thomas would probably be the most likely ones to have moral concerns with letting her die, but I can't imagine Scalia not teeing off on Congress for creating this massive exception to ordinary rules of federalism.
If I were guessing, I'd say Rehnquist and O'Connor would be most likely to do anything. None of the liberals are likely to want to play the game (maybe Stevens, but I doubt it).