Seriously. Georgia did it in the Cherokee cases — they raised their sovereign immunity defense and literally filed no briefs and made no appearance at oral argument. [Of course, that wouldn’t happen now if a party refused to appear — the Court would appoint counsel to argue the case.]
It would be a radical move, and must be strategic. My guess is the best (and perhaps only) time to try it is when the Supreme Court accepts jurisdiction over a case entirely under its common law jurisdiction. An example would be the Court’s review of tribal court jurisdiction over nonmembers, reviewable not through authorization from Congress but solely under the Court’s decision in National Farmers Union, which created both a federal right and a federal remedy. Federal courts could still properly review tribal court jurisdiction when a party is seeking to enforce a tribal court order in federal court.
Or maybe the boycott should occur where the Court is reviewing treaty language, as Rob Porter and others have suggested.
The main problem here is that tribal interests want to win these cases, and, well, they won’t if they don’t show up. So we’ll keep following the Supreme Court, which will issue some orders later today that may affect Indian Country.