We're talking about moderate Republicans, of course. That doesn't mean they're welcomed these days in their own party, though.
Out in California, a former Arkansan and Marine Corps war hero named Nathan Fletcher ran for the state house and won a few years back, and has since distinguished himself by being a moderate Republican willing to work with Democrats in the statehouse and Governor's office (see his speech against "Don't Ask Don't Tell").
Now he's running for Mayor of San Diego, and has received such a drubbing from the local GOP — including their decision to endorse a candidate whose politics are more in line with Right Wing dogma — that he's decided to leave the party and run as an Independent. In the video announcing his decision (seen above), Fletcher says he believes he could win as a Republican, but is leaving the party because it's clear to him that partisan politics is "an environment that thrives on playing the game."
David Brooks with the New York Times comments on Fletcher's decision to bail on red and blue.