I'm going to start with this - I really don't see any sign that McCain had any interest in playing to the usual racist rubes that were bound to pop up in reaction to Obama's nomination. If anything, he was positioning himself to snatch up black voters up until it became clear that the Democratic superdelegates were not going to overturn voters and give the nomination to Hillary.
Moving on...
This is, at it's heart, another one of those common tactics when it comes to discussing race in the US. Person A makes a plainly racist statement about how one race is violent, lazy, or greedy - as has been a common claim from the right-wing since Obama became a presidential frontrunner.
Person B hears the claim, and points out the obvious racism behind claims that Obama couldn't have written his book or received his grades (Trump), or that black people are "satisfied with food stamps" (Gingrich) or "taking other people's money" (Santorum) or had stronger families under slavery (Bachmann), or that black people who vote for democrats are akin to thoughtless plantation slaves (Cain*).
Person C then becomes outraged, because calling someone a racist is the lowest of possible insults. Lower than rapists, thieves, murderers, child sex predators, or genocidal maniacs. Basically, they hear the word "racism" and rush to the fainting couch. Note that this isn't always a conservative - there are plenty of liberals that also fly into a rage at Person B, such as Geraldine Ferraro back in 2008, or supposedly neutral people like Tom Brokaw in 2012.
Obviously, "Joe" "The" "Plumber" is Person C in this too-common scenario. he may or may not be a racist himself, but he's instead playing defense for racism, under the misguided belief that B calling a specific person a racist, is worse than A proclaiming an entire group of people as inferior based entirely on perceived race. A basic glance at US history should prove to every reader that the opposite is the case. SO I can't quite say that "Joe" is a racist himself, but he's clearly using a disingenuous apology for it.
I won't even bother with his yammering about Reagan, since, well, I remember growing up in the Crack Era that was the 1980s, and being told by white people that my mother was a "welfare queen" despite her holding a Master's degree and a lecturer position at a university.
*: Yes, Herman Cain is black. So was William Hannibal Thomas.