If Remnick asked, "Aren't most of the people who oppose you motivated by race?" then a response that some people may oppose him because of race and others favor him because of race doesn't seem to be entirely out of place.
It's the kind of answer politicians like -- not exactly an affirmation, not exactly a negation, not especially gracious or ungracious, more a brushing away of a question the politician doesn't want to answer than an actual response.
Of course, that may not be the context, and the blogger may be right about this -- it might be Obama hiding behind race again and lashing out at his opponents -- but that's not the only answer. If he really wanted to lash out, he could have gone further.
Some politicians avoid the New Yorker because it doesn't let their remarks stand as written, but works them into contexts that are the writers' own creation. To be sure, Remnick and Obama are on the same side politically, but Remnick is hung up on a particular narrative here and he's going to write his article to reflect that story.
It is clear as crystal that 0bama is a racist and a whining excuse maker.