I don't know if there are any dates before the end of this term for SCOTUS to delay this decision. I don't know if EWTN must comply immediately or not with this judge's decision.
If they appeal, don’t they get an automatic stay?
Worst case scenario: They simply do not obey an evil mandate.
From the EWTN site:
Irondale, AL (EWTN) “We are extremely disappointed with the decision reached by the court in this case. The opinion issued is clearly inconsistent with the decisions reached in nearly all of the cases decided to date. The fact that the court has dismissed the serious issues of conscience and religious freedom that EWTN has raised is very troubling.
As an organization that was founded by Mother Angelica to uphold the teachings of the Catholic Church, we do not believe that contraception, abortion-inducing drugs and voluntary sterilization should be defined as health care. We simply cannot facilitate these immoral practices. We have no other option but to continue our legal challenge of the mandate. We are making an immediate appeal to the Eleventh Circuit Court of Appeals in Atlanta.”