Yes – I believe they had a ruling on that once.
Of course, that lack of authority on the government’s part also extends to their attempts at controlling people’s personal property i.e. Universals Gun Registration.
United States v. Lopez, 514 U.S. 549 (1995) invalidated the Gun Free School Zones Act as an impermissible exercise of the commerce clause power. In it's opinion, the Supreme Court instructed Congress how to draft a Gun Free School Zones Act that would survive judicial scrutiny, and be a permissible use of the commerce clause power.
All Congress had to do was add the phrase "or affects", preceding "interstate commerce."
Scalia is a big fan of this extension of federal power. He used it to uphold federal prohibition on pot in the Raich case. It was also used to reverse a gun case (not school zone), after the 9th Circuit found that a homemade gun, that never left the state, isn't an object of interstate commerce.