International Obligations and Domestic Implementation
This dichotomy suggests that it is possible for the U.S. to be in plain violation of international law, but for there to be no domestic remedy for the international law infraction. Bradley admitted a number of times that he thinks both that the Vienna Convention Treaty is self-executing and that the U.S. is in violation of international law. His point, however, was that although the ICJ ruling was a proper interpretation of the treaty for U.S. international obligations, it was not, itself, a treaty and is, therefore, not the "supreme law of the land."
Professor Damrosch doesn't seem to disagree. I don't think that she sees the ruling as itself being a new treaty, but that the ICJ ruling changes both the international and domestic substance of the treaty.
She wants to import the ability of the ICJ to interpret the U.S.'s international law obligations into the domestic sphere, allowing the ruling to also interpret the treaty's domestic effect. For her, the disconnect between the international obligations and domestic implementation undermines the structure and validity of the international legal system. She wants to remedy this, not by trying to convince congress to pass a statute clarifying the domestic nature of the treaty or by convincing the Supreme Court to agree with the ICJ and itself interpret the treaty the same way the ICJ did, but to require the Supreme Court to be bound by the ICJ ruling.
Professor Damrosch advanced a number of political arguments, that the U.S. needs to honor its treaty obligations, follow the ICJ interpretation ruling, because we benefit from the treaty protocol. But the argument must be constitutional--she has to show how the President and Congress can get around Marbury v. Madison by signing a treaty with a compulsory juridiction clause. She has to show how congress can vest legal authority in an international body without any review. These are arguments, it seems, she can't make. Instead, I think, she conflates the interpretation of U.S. international obligations and the domestic implementation.