The Tenth Amendment says the federal government can only do things expressly listed in the Constitution -- every other federal activity is illegal.
That list, in entirety:
1. Mint gold and silver coins (*not* paper money)
2. Establish citizenship rules
3. Post offices and post roads
4. Bankruptcy, counterfeiting, piracy laws
5. Patents and copyrights
6. Regulate commerce with foreign nations, between states, and with Native tribes
7. Declare war; maintain army, navy, and militia
8. Establish lower federal courts
9. Exercise authority over Washington, D.C.