Final answer:
The Supreme Court would likely deem a school football coach leading his team in a prayer as unconstitutional based on the establishment clause of the First Amendment.
Step-by-step explanation:
In the case of a school football coach leading his team in a prayer, the Supreme Court would likely deem it unconstitutional. The Court has consistently ruled that prayers organized or facilitated by school authorities, even as part of off-campus or extracurricular activities, constitute an illegal establishment of religion. This is in line with the establishment clause of the First Amendment, which limits official endorsement of religion. Examples of cases that support this include Engel v. Vitale, where the Court ruled that requiring students to recite a prayer written by the state was unconstitutional.