Yes, it's the expansive interpretation of the Commerce Clause. This is the Supreme Court case that fully fleshed out that doctrine:

https://en.wikipedia.org/wiki/Wickard_v._Filburn

Basically, if they can somehow connect it to interstate commerce - even if it very indirect, like in this case where growing something for personal consumption affected demand - it's "constitutional", supposedly.

This is the case that explicitly extended this reasoning to drugs:

https://en.wikipedia.org/wiki/Gonzales_v._Raich