Over at LewRockwell.com, Laurence M. Vance writes:
Under the Constitution, the federal government has no authority whatsoever to ban high-power weapons, high-capacity weapons, high-tech weapons, machine guns, automatic weapons, armor-piercing bullets, "cop-killer" bullets, sawed-off shotguns, assault rifles, gun sales to felons, bazookas, armored personnel carriers, grenades, IEDs, bombs, or tanks. ... Permitting or prohibiting these substances is a matter for each individual state to decide.
It is true that there are some matters which the Constitution leaves up to the states. Where it does so, it specifies either that those are state matters, or just that they aren't federal matters.
With respect to the right to keep and bear arms, however, the constitutional provision regarding keeping and bearing of arms is very specific. The 2nd Amendment recognizes that right as a "right of the people," not a power of the states (see the 10th Amendment for another instance of this distinction), and prescribes that it "shall not be infringed," period.
Not by the congress.
Not by the president.
Not by the governors.
Not by the state legislatures.
Not by anyone.