From SCOTUS case Lemon v. Kurtzman.
Click through for details, but Warren Burger set important guidelines on how First Amendment cases dealing with the establishment clause should go foreward.
The three criteria which Burger laid down in his decision are very important in all such cases where there are possible establishment clause entanglements.
Here it is, from Wiki:
The Court's decision in this case established the "Lemon test", which details the requirements for legislation concerning religion. It consists of three prongs:
1. The government's action must have a secular legislative purpose; (Purpose Prong)
2. The government's action must not have the primary effect of either advancing or inhibiting religion; (Effect Prong)
3. The government's action must not result in an "excessive government entanglement" with religion. (Entanglement Prong)
If any of these prongs are violated, the government's action is deemed unconstitutional under the Establishment Clause of the First Amendment to the United States Constitution.
It is easy to defeat this challenge just on the first prong, as there is no way the arguments serve a secular purpose as virtually every argument against these ACA provisions are made in a religious context.
It also fails the second prong, although that's not obvious. One could argue either way, I suppose, but I do not think that the ACA opponents will deign tread down that path.
The third prong is fatal to the ACS opponents. There is no way that anybody could credibly argue that if SCOTUS rules for the ACA opponents that they would not be entangled with religion again and again, as other DU posts argue. Jehovah Witnesses and transfusions; Scientologists and mental health; Christian Scientists and reality!
I really hope this challenge fails. If it doesn't it might mean that Lemon is dead. That would be very bad.