No. Because the first amendment says, "Congress shall make no law ...". It's right there. Plain as day.
Did you see something that said Congress cannot prohibit the interstate commerce of machine guns? They've been doing that for over 70 years and no one's caught it yet.
But, wait! YOU found something?!?!
No they have not, they've been taxing commerce in machine guns for over 70 years, and the Supreme Court has never ruled on the practice, Miller being the only National Firearms Act case to reach the Supreme Court.
Actually they've been prohibiting the commerce for 21 years, but only for newly made weapons.