Except that under the Constitution, they can't do it via the 1st Amendment. The 1st Amendment is self-executing, meaning Congress has no enforcement power - you just have a right to sue for violations of it by virtue of the fact that it exists. Enforcement powers are generally reserved for the Civil War Amendments (13, 14, and 15), and even then, the most potent provisions generally only apply to state actors (with some exceptions). Again, the law in question is not 1st Amendment-based, but likely commerce clause-based, as I said earlier.