A remarkably high amount, at least in 2008. He would not have come anywhere close to winning Missouri otherwise.
I've told this story before, but - I once read about the experience of a campaigner or pollster or something in rural PA in 2008. He knocked on a door and asked the couple who answered who they were voting for, and the man said "we're voting for the n*."
So, yes, a lot. Obama was "one of the good ones," apparently.
I read about this happening (I believe on Quora) but in Indiana.
It was in fact
in PA:
So a canvasser goes to a woman’s door in Washington, Pennsylvania. Knocks. Woman answers. Knocker asks who she’s planning to vote for. She isn’t sure, has to ask her husband who she’s voting for. Husband is off in another room watching some game. Canvasser hears him yell back, “We’re votin’ for the n***er!”
Woman turns back to canvasser, and says brightly and matter of factly: “We’re voting for the n***er.”
My interpretation of this is not that these individuals in 2008 thought Obama was a reasonable black person or whatever, but that they instead blamed the 2008 GFC on Republicans and the Bush administration and that this was their top issue that year, so they voted for Obama as a protest vote. I think this interpretation would explain why that year was a huge wipeout for Republicans at all levels; the GCB was D+10.6 which beat Obama by about 3 points.