I watched the first day argument in the entirety on Cspan. The discussion was much more abstract than any of the interpretations that I've seen or heard in the media. The gist of the discussion:
The long-run implications are really for other tax cases. If the AIA were non-jurisdictional, then it is both subject to waiver and the creation of judicial equitable exceptions, and thus any tax might be challenged before it was assessed, if the government failed to raise the AIA bar or the courts found an equitable exception.
(AIA - Anti-Injunction Act)
Clearing away all of the rest of the discussion, I believe the case will be settled on this point of law. As with the Citizens United decision, the ramifications of the decision will probably not be connected to anything that resembles the public good, or the moral high ground, but rather like a game, that uses words and theory to determine the intent of previous legal determinations.
Nine people trying to avoid a gotcha.