I think it would also be interesting to pick the county that voted most unlike the rest of the state that also has the most people. I think those counties would be more "unhappy" because they have the most residents that voted against the state winner. So, some examples:
California: Orange County/ 1,122,664 votes /53% Romney
Georgia: Dekalb County/ 306,858 votes/ 78% Obama
Ohio: Butler County/ 170,530 votes/ 62% Romney
Texas: Travis County/ 387,057 votes/ 60% Obama
Colorado: El Paso County/ 290,175 votes/ 59% Romney
West Virginia: Kanawha County/ 75,312 votes/ 55% Romney
It doesn't work as well for every state and a lot of it is up for debate but I think it's interesting to look at.
Interesting, my question for this though, would be are we directly combining the elements of large population and large % margin somehow, or is it just the largest county that voted against the state winner? With the latter I could say Harris County, TX is the unhappiest of the counties in Texas just because its the largest although it only went to Obama by under 1,000 votes and 0.1%.
For the former we could just use county vote margins (winner votes minus loser votes). Since Dallas County, TX has the highest Obama vote margin, it could be considered the most unhappy county. Same with Sioux, IA even though its not the most populated county to vote for Romney.