Just to repeat, the Court has two other (reasonably important) decisions to hand down on Thursday: First American Financial Corp. v. Edwards and United States v. Alvarez. The practice at the Court, as most of you know, is to announce decisions in the reverse order of the author's seniority.
Because he is the only Justice yet to author a majority opinion from the December sitting, it seems quite likely Thomas is the author of First American Financial. (Because his views of Article III standing might be a bit miserly compared to his colleagues, however, it is possible his opinion will only represent a plurality--which would explain the delay in that opinion. Regardless, he would announce the Court's judgment from the bench, even if parts of his opinion did not garner five votes.) It is also likely that either Kennedy or Kagan has Alvarez, as neither of them has authored a majority from the February sitting. (My guess is that it is Kennedy, trying to fashion a narrow rationale based on the trademark-brand dilution idea he floated at oral argument.)
Further, as discussed yesterday, it is almost certain that the Chief Justice has the Court's opinion in the health care cases--or at least the opinion addressing the constitutionality of the minimum coverage provision.
If we put all of this together, it means that we will probably get the health care opinions at about 10:15 EDT on Thursday, as the announcements of First American Financial and Alvarez (whether by Kennedy or Kagan) are apt to come first.
This raises an interesting question. Suppose that a justice other than the Chief is authoring the Medicaid opinion. Technically, that opinion should be announced first. But if it were, it would give away at least part of the result in the other case, as it would at least reveal that the entire ACA had not been invalidated (i.e., it would reveal the result of the severability question). My guess, then, is that the Medicaid opinion would likely be announced second--regardless of the author (and assuming there is separate opinion in 11-400). And perhaps the point will be moot because the Chief has assigned both opinions to himself.