Obama performed better with whites in Ohio than nationwide, because of the auto bailout.
Republicans tend to rack up huge margins amongst Whites in the South so this skews the results. In Indiana which is a reliable red state in most elections (2008 was somewhat a fluke), the percentage of whites who voted for Obama was pretty much bang on the national average and slightly better than what Obama got in Virginia and Florida (both states he won). Gender gap may partially explain as amongst white males Romney won by a landslide in Ohio, while it was much closer amongst white females. It seemed the gender gap was much larger in the northern states than southern states and I suspect some of the talk on legitimate rape and anti-abortion hurt the GOP amongst female voters. In fact Steve LaTourette's wife was planning to vote for Romney, but then voted for Obama after the rape comments so I suspect there were other women who had the same issue.