In D.C. vs Heller SCOTUS held in it's majority opinion that "Like most rights, the Second Amendment right is not unlimited. It is not a right to keep and carry any weapon whatsoever in any manner whatsoever and for whatever purpose"
So yes according to SCOTUS interperation of the 2nd Amendment it is constitutional to place limits on firearm possesion. Of course SCOTUS has left it open as to what those limits are. It will be up to further cases to start figuring out what those limits are.
Jerry Brown actually wrote a "friend of the court" brief in favor of Heller in that case.
In fact, in his veto message of 374 (weapons ban), he references the Heller ruling, by using the phrase "Common Use" when discussing the rifles.
As moonbeamy as he is, he thinks things out at least.
On a side note, a court in Illinois is pushing Heller even further:
"As the Seventh Circuit correctly noted, neither Heller nor McDonald expressly limits the second amendment’s protections to the home. On the contrary both decisions contain language strongly suggesting if not outright confirming that the second amendment right to keep and bear arms extends beyond the home. Moreover, if Heller means what it says, and “individual self-defense” is indeed “the central component” of the second amendment right to keep and bear arms, then it would make little sense to restrict that right to the home, as “[c]onfrontations are not limited to the home.”
http://www.thetruthaboutguns.com/20...rt-right-keep-bear-arms-extends-outside-home/