This is the other case in the Sixth Circuit. The District Court for the Northern District of Ohio, a while back, rejected the challengers claims that the ACA violated (1) their fundamental rights protected as a matter of due process, (2) their constitutionally protected rights to expressive and intimate association, or (3) their constitutional right to privacy. The court then permitted the plaintiffs to pursue an appeal on those claims, while it held onto the claim that the minimum coverage provision exceeded Congress's enumerated powers. Two days after the Sixth Circuit's decision in Thomas More Law Center, the court dismissed that last claim as well.
The plaintiffs' appeal is now pending in the Sixth Circuit. Obviously, unless the Sixth Circuit votes to take the question en banc, the plaintiffs' claim concerning the minimum coverage requirement is now foreclosed by circuit precedent. But the three other claims remain live (however improbable).
You can find the plaintiff-appellants' brief here. And you can find the United States's brief here.
The plaintiff-appellants' reply brief is due Monday (July 18), which will complete the briefing in the case. At that point, the Sixth Circuit will presumably calendar the case for oral argument.