They have whatever power the Supreme Court decides they have. The Supreme Court decided that was their job, and thus far everyone has accepted it. The Court interprets the Constitution, which is vague enough to mean whatever a bare majority wishes it to mean.

And then they reversed course with Wickard v. Filburn and said it was perfectly OK for Congress to regulate, not just commerce within a single state, but farmers growing their own food on their own land for their own use. So FDR ended up getting what he wanted anyway.