In March 2010, a Pew survey asked "Would you favor or oppose allowing an American state to secede and become independent from the country if a majority of the people from that state wanted to do this?" About 25% were in favor. People with favorable attitudes towards the Tea Party movement were more likely to be in favor. Beyond that, however, there were some surprises. Because the only serious attempt at secession was the Confederacy, you might expect opinions to differ by race and region, but they didn't. People who said that they were "very conservative" were most likely to be in favor, but the next most favorable group was people who said they were "very liberal" (moderates were least favorable). Younger people were more likely to be in favor, and more educated people less likely.
The association with education is interesting because more educated people are usually more likely to favor individual choice and to put less weight on tradition (e. g., educated people are more likely to be in favor of same-sex marriage). That tendency would suggest that educated people would be more favorable, on the grounds that the people of the state have a right to make whatever choice they want. It could be that educated people are more likely to think of potential problems with that logic--e. g., a majority ethnic group that wanted to be able to oppress the minority. Or maybe more educated people tend to be more "cosmopolitan," and think that larger political units are superior to small ones.