McCain's problems with the base from 2000-2003 or so were actually far more significant than Christie's current problems, in large part because they were both substantive and symbolic, whereas with Christie it's more symbolic. Read Jonathan Chait's 2000 column "This Man is Not a Republican":
http://www.newrepublic.com/article/politics/man-not-republican#By 2002, he was cosponsoring virtually the entire Democratic domestic agenda in the Senate, and people were urging him to run for president in 2004.....as a Democrat:
http://www.slate.com/articles/news_and_politics/chatterbox/2002/04/come_home_mccain.htmlIn 2004 though, McCain appeared to make a decision that he could still be president, and the best means by which to reach the White House was via the GOP nomination, so he began a program of systematically un-mavericking himself. Christie may very well do the same after he wins reelection by an enormous margin. We'll see. Obviously, that's a bit later in the cycle than what McCain did, so it may or may not work.