Transcript Supreme Court argument
It's here, in pdf. Argument centers around a treaty requirement that consulates be notified if their nationals are arrested, an important consideration being the power of the International Court of Justice to make a ruling, and how much that ruling obliges US courts to follow it in these circumstances (which I don't understand, but apparently the president did something to make it arguably binding).
As usual, it was less an argument than a grilling. Counsel for the petitioner seems rather underprepared. Watch the dynamics. CJ Roberts pins him on a hypothetical (if the ICJ not only made a finding, but ordered the violators imprisoned, would that also bind US courts?). The hypothetical interests Kennedy, whom Roberts is likely courting as a swing vote. The attorney can't come up with an answer, but Ginsburg tries a "save" by suggesting one. Again he gets stuck, and Breyer tries for a save. Alito comes in, and Kennedy and Roberts go back to tag-teaming him.