Move massively to the left. That is the lesson of the Govenator's 2006 reelection, standing proud and true among the Republican wreckage.
Now some will try and spin Schwarzenegger as moving to the "center" but the truth is after his own "thumping" in the 2005 special election, he has been firmly planted on the left. His chief of staff is now an out lesbian, former chief of staff to Grey Davis. In fact, he pretty much working the exact same ground that Grey Davis did.
He's put in big spending increase for education and campaigned (successfully) for a host of bond measures to massively increase infrastructure spending. He's signed a minimum wage increase and a global warming measure. He's said US troop should come home from Iraq. Sure, he's gotten wormy about finances in order to offer no tax increases, but it’s not like Grey Davis didn't play these exact same games.
So given the fact that policy-wise Schwarzenegger is indistinguishable from a Democrat, why not vote for the global celebrity? Its fun. It’s funny. It only stops being funny when Schwarzenegger actually acts like a Republican. Now he knows better.
The same California voters just elected Jerry "Moonbeam" Brown Attorney General by an even larger margin that Schwarzenegger won. Donkeys won for Lt. Governor, SecState and Treasurer, not to mention kept large margins in both houses of the State Assembly and Senate. The Govenator is a party of one.
The lesson of Schwarzenegger is act like a Democrat, get elected like a Democrat. I seriously doubt that this is a model the GOP can export to the rest of the Country.