I did the math, and it looks like Romney won white voters in the south as a whole with 71% or 72% to Obama's 27%. Even with that, the South only makes up about 30% of the nation's white votes, so whites outside the south are still Republican (probably about 54% Romney). They're Republican everywhere outside New England and the West coast. So yeah, the Democrats have a white problem. And its natural (if elections were to maintain competitive) that if Democrats get a big majority of the non white vote that is increasing in its share in the electorate, that they also lose support from white America.
I'm pretty sure at some point the Republicans will hit a ceiling with the white vote, since there is a significant segment of the white vote that will flat out never vote Republican, mainly the white liberal types that support Sanders and people like that. Also it's pretty normal that white people in large cities tend to lean Democrat, not just the northeast and the west coast. Even the white population in the immediate Atlanta area voted for Obama I think, not sure about that.
You're right, I was broadly saying it on a state by state basis, but big cities in states where Romney won the white vote are definitely D leaning in most cases. White vote will hit a ceiling, but really how much more vote can Dems get out of Blacks, Hispanics, and Asians? Obama pretty much maxed out with those groups, while the white vote can and has been up to 65% for Republicans. So while I think the Republican ethnic diversity problem is worse, Dems still have an issue with white voters, especially white working class voters, which should be MUCH more Democratic than they currently are.