It's ironic that winning an extraordinary amount of Democratic support in his re-election bid would probably hurt him in the Republican primary. Even if he doesn't win the nomination, he has to go down as one of the most successful blue-state GOP governors in recent history.
The GOP's last four nominees were all known for receiving substantial cross-party support in their most recent election campaigns. Like everyone, Republican voters like a winner. They less tolerance for pandering to one's opponents, but considering that the aforementioned Dole/Bush/McCain/Romney all did just that, it's not really that big a deal.