Unfortunately, it looks like the Supreme Court thinks Congress has this power too. From Quill v. North Dakota:
This aspect of our decision is made easier by the fact that the underlying issue is not only one that Congress may be better qualified to resolve, 10 but also one that Congress has the ultimate power to resolve. No matter how we evaluate the burdens that use taxes impose on interstate commerce, Congress remains free to disagree with our conclusions. See Prudential Insurance Co. v. Benjamin, 328 U.S. 408 (1946). Indeed, in recent years, Congress has considered legislation that would "overrule" the Bellas Hess rule. 11 Its decision not to take action in this direction may, of course, have been dictated by respect for our holding in Bellas Hess that the Due Process Clause prohibits States from imposing such taxes, but today we have put that problem to rest. Accordingly, Congress is now free to decide whether, when, and to what extent the States may burden interstate mail-order concerns with a duty to collect use taxes.
I'm not sure what to think here. It seems like this law would be enabling states to enact protectionist mercantile policies that make shopping at out of state retailers more expensive than shopping in state. Now you have to pay tax AND shipping. My guess is that this will cause Internet companies to start setting up shop outside of the US...leading, naturally, to the Feds enacting tariffs on goods purchased over the Internet. Let's hope this dies in the House and we don't have to find out.