First, it is worth noting that, in its motion to dismiss, the government argued that the plaintiffs' challenge to the individual mandate was barred by the AIA (a position that it has since abandoned). Second, Judge Conner rejected the AIA argument on two grounds:
1. He concluded that the mandate itself is not a tax, as all it does is command individuals to purchase health insurance.
UPDATE: In light of several thoughtful comments I have received today, I would like to retract part of what I have asserted here. The essence of my point was, and remains, that I am not sure it makes any sense--for purposes of evaluating whether a suit to enjoin the individual mandate is barred by the AIA--to view 1501(a) (which imposes the legal liability to acquire health coverage) independently of 1501(b), which imposes the exaction for the failure to fulfill that obligation.
2. Alternatively, he concluded that the exaction imposed by 1501 is a "penalty," and not a tax, and the AIA only applies to "tax[es]." Again, the term "any tax" in the AIA may well not include the exaction imposed by 1501. But it cannot simply be because that exaction is a "penalty." Indeed, as Judge Motz's opinion in Liberty University demonstrates, the AIA plainly applies to many "penalties" imposed by the Internal Revenue Code. Moreover, Judge Conner relies heavily on reasoning (used by other courts in the ACA litigation) as to why the exaction imposed by 1501 is not a "tax" for purposes of determining whether it falls within Congress's taxing power. But again, as the Bailey cases illustrate, the definition of a "tax" under the AIA is broader than that under the General Welfare Clause (which is fairly broad to begin with).
In short, the analysis in Goudy-Bachman as to why the AIA does not bar jurisdiction appears to be lacking. That is not to say that AIA does pose such a bar. Rather, the point is that the courts coming out this way have not really matched the analysis of Liberty University.