Why Medellin is Making the Wrong Argument
I note below that Professors Bradley and Damrosch agree that the ICJ ruling is binding on the U.S. international obligations. Where they disagree is whether that ruling should flow through, and also bind the U.S. domestically.
But when pushed last night, Professor Damrosch agreed that the Supreme Court would not have to uphold a ridiculous ICJ ruling. For instance, if the ICJ interpreted the Vienna convention not to just require the notice to the consulate, but to abolish executing foreign nationals altogether, even Professor Damrosch (it seems) would agree that this ruling should not "flow through" the way she thinks Avena should.
What this means (I think) is that Professor Damrosch is not arguing that ICJ rulings are automatically binding--what she seems to suggest--but that there should be a sort of Chevron deference to the ICJ interpretation of the treaty. In a situation as we have here, where it's clear that the ICJ is right that the U.S. is in violation of its treaty obligations, the Supreme Court should be bound to give some deference to that body. But when the ICJ over-steps its bounds, the Supreme Court can overrule its findings.
This would not be an awful argument. Marbury certainly isn't the last word, as Chevron makes clear. The meaning of statutes can, in some circumstances, come from non-Article III judges without offending Marbury's famous holding that "[i]t is emphatically the province and duty of the Judicial Department to say what the law is." But this is a very different argument. And there are certainly problems with extending the domestic non-Article III adjudication jurisprudence to the international sphere where there is less political accountability and decision-making transparency, as I noted here.