There are two factors:
- genuine, bona-fide racist white people, who think they benefit from racism, and who feel entitled to benefit from it at the expense of people from other ethnic backgrounds, and who resent the real advancements in opportunity achieved by and for Americans of other colours. Hi there, confederate states, how're ya doin?
- non-racist or even anti-racist white people, who are tired of hearing from some activists that they have some kind of golden ticket "white privilege" when in fact racism has never given them anything, who are provoked by a very small number of anti-white racists, and who are voting not based on race but in a political act of self-preservation.
Clearly millions of white people are happy to embrace equality and happy to see other ethnicities do well, and happy to vote people into positions of power regardless of ethnicity. Obama's results show that.
But white people who have never benefitted from racism will never accept the misguided arguments for dismantling racism that are made by some people. In addition to challenging actual acts of racism, the first thing that has to go is the term "white privilege." For something to be called "white privilege" it would have to be true of all white people, and that is just a fantasy or a lie.
Here's a group of white people with no "privilege." http://www.bbc.co.uk/news/education-20898608
White working-class boys in the UK (the country that invented white colonialism) do worse than, and have fewer opportunities and resources than, any other social grouping in the United Kingdom. Tell those people they have privilege and watch them laugh in your face. Be ready to run, though.
If you want white people to be part of the solution to racism, it's far better to talk about "elite privilege." That is a more accurate term to describe the phenomenon, where it still exists. And it has the advantage of not disenfranchising the millions of white people who are still waiting for their supposed gift-pack of extra white goodies and scratching their heads while a vocal few accuse them of having "privilege."
Basically if someone's anti-racist spew convinces white people that they do indeed benefit from racism, then it doesn't take a genius to figure out that many of them will support actual reactionary racist policies and candidates. The language of fairness is faaaar more powerful than the language of privilege in addressing this issue.