Impeach Governor Schwarzenegger?

Governor Schwarzenegger has just signed into law a bill that directs makers of violent video games to label those games prominently with the number 18, and that forbids the rental or sale of such games to minors.  The story is here.  I've looked at the legislative language, and although it makes some effort to tie the law to Supreme Court decisions in the area of obscenity and minors (and, more peculiarly, as an alternative approach, to cases discussing "heinous, atrocious or cruel standard in capital cases), the law will, more or less beyond a doubt, be found unconstitutional on either state or constitutional grounds, both for vagueness and/or overbreadth and as an impermissible content-based regulation of speech.  Similar statutes have faced that fate in federal court; see, e.g., Interactive Digital Software Ass'n v. St. Louis Cty., 329 F.3d 954 (8th Cir. 2003); American Amusement Mach. Ass'n v. Kendrick, 244 F.3d 572 (7th Cir. 2001).  In the Ninth Circuit, a similar law was invalidated by a district court in Washington state; see Video Software Dealers Ass'n v. Madeng, 325 F. Supp. 2d 1180 (W.D. Wash. 2004) [cite info may be slightly off on this last one].

How can the Governor -- who signs a bill to support the Constitution -- defend signing this bill, which is fairly transparently unconstitutional?  (Professor Kevin Saunders, a professor at Michigan State's law school who has been an advocate for restricting such materials aimed at minors, says in the article that "[t]he fact that previous courts have struck [such laws] down doesn't mean a court with more evidence won't uphold it"; I think he is engaging in wishful thinking.)  We've talked some about oaths and oath-keeping on this blog; this is another example.  Of course, the Governor might believe the courts have wrongly interpreted the First Amendment and that the bill is constitutional on a proper reading of the state and federal constitutions; or that loyalty to the Constitution is consistent with signing laws whose constitutionality is dubious and leaving it to the courts to resolve the issues -- although that is not exactly the essence of conservative thinking on this issue.  More likely, the Governor either thinks the law is unconstitutional but doesn't care, or just doesn't care one way or the other.  There is always much talk about the need for loyal and self-restrained judges and Justices who respect the Constitution.  Would that there were more discussion of the oath-bound obligations of elected officials.

P.S.:  I am looking forward to reading of the enterprising reporter who seeks the Governor's explanation as to whether a law that imposed similar age restrictions on moviegoing for violent films would be equally constitutional.  Could the state bar 17-year-olds from renting or attending or purchasing Terminator 3?  (Or just about any other Schwarzenegger movie.)  If the video game law is a good idea, wouldn't a similar measure for movies be equally good public policy?  When will the Governor be pushing this legislative measure?