It should be noted that the U.S. has apologized for its mistake in not granting consular access to the individual who was convicted and later executed. That was a procedural error. However, it was not an error that compromised the defendant's access to due process.
In Medellín v. Texas (2007), the U.S. Supreme Court denied the petition to block the execution on a number of substantive grounds:
1) The Vienna Convention's language did not have the force of law--in other words, specific self-executing provisions--under which the domestic legal process would automatically be stopped or reversed were consular access mistakenly not provided.
2) Congress did not pass legislation that was enacted into law providing a specific remedy for such circumstances.
3) The defendant's confession was not obtained unlawfully.
4) The defendant was not deprived of adequate legal counsel.
Given the above findings, whatever one's position is on capital punishment, I don't believe the U.S. Supreme Court could have reached a different conclusion. Outside requests on the issue were, at best, properly treated as advisory in nature. Those making the requests lacked jurisdiction.
Indeed, were jurisdiction expanded to those bodies by the U.S. Supreme Court, it would have established a dangerous precedent that would have undermined the sovereignty of the U.S., eroded the preeminence of the U.S. Constitution, and diminished the role of U.S. representative government. In my opinion, that precedent would have been far more damaging, for the U.S. and any other sovereign state, than the political fallout that has resulted from the decision.
Personally, I would have preferred that adequate consular access had been provided and the error avoided. However, I believe the U.S. would have made a grave error had it effectively established a precedent that limited its sovereignty, reduced the paramount role of its Constitution as the ultimate source of its legal authority, and undermined the authority of its representative institutions by permitting an outside unelected body the ability to override authority that properly rests with the domestic institutions of a sovereign state.
All said, on this matter, even as I fully support Article 36 of the Vienna Convention, I would err on the side of preserving sovereign authority. That was the much larger and more important issue at stake.