Electoral College challenge

I have been following this a bit, but I missed this yesterday. The NY Times reported that California Gov. Schwarzenegger vetoed a bill that would have given all the state's electoral votes to whichever candidate won the national popular vote.

I'm no fan of the Electoral College, and I'd like to see it done away with completely, but I'm not sure this is the way to do it. Since California is a reliably Democratic state, this kind of unilateral change could only stand to help a Republican who won the popular vote but failed to carry California's vote.

That said, I am all for a constitutional amendment that would dispense with the Electoral College and simply elect the president through the national popular vote.