From the 2008 DC v. Heller ruling, written by Scalia, and one of the very few Supreme Court cases to touch on the Second Amendment at all:
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: For example, concealed weapons prohibitions have been upheld under the Amendment or state analogues. The Court’s opinion should not be taken to cast doubt on longstanding prohibitions on the possession of firearms by felons and the mentally ill, or laws forbidding the carrying of firearms in sensitive places such as schools and government buildings, or laws imposing conditions and qualifications on the commercial sale of arms.
Remember: Written by Scalia, i.e., not one of those liberal judicial activists you hear so much about.
There is no constitutional bar to some limitation and regulation of firearms. The real question — the only real question, to my mind — is whether there is the political will for it.