This all comes down to what we mean by "intensely demonstrated". Maybe I'm just sensitive, but the demonstrations that have struck me as particularly "intense" have also struck me as particularly racially motivated. Maybe that's just my personal experience with the inbred trailer trash I see making those demonstrations talking. But the kinds of "intense demontrations I think he's talking about are of the sort shown in that video, with the white-face Joker posters, the Nazi name calling, etc. That kind of vehemence doesn't come from mere political interest.
Are you disputing the word "many" here? Are you disputing that there are even "many" racists in America?
A statistic I'd attribute to the fact that most of the country is white. What you want to be asking yourself is what percentage of the country is racist, and then what percentage of those racists voted for Obama, and then, therefore, what percentage of the people against Obama are racist.
For instance, somewhat recent polls indicate that 13% of white Americans say they are "racially biased" (i.e. racist). Those are the ones that admitted it and recognized it. I think it's safe to say that the real number higher, probably not insignificantly higher. So, assuming a 50-50 split among whites for the vote and further assuming that none of the racists voted for Obama, that makes the anti-Obama racist percentage somewhere around 25%, or 1 in 4.
Does this mean that Jimmy Carter is right? Not by itself. But simple parsimony would suggest that the level of vehemence we're seeing in a crowd composed of at least 25% racists, holding their racist signs and accusing Obama of being a foreigner, of being a muslim, or being racist himself.... it certainly makes Carter's suggestion a bit more than merely plausible.
Ancedontal evidence is not evidence, but I'm pretty sure the fact that I'm surrounded by racists bitching about Obama in Pennsylvania, who fought on the side of the North in the Civil War, means that this is happening everywhere to some degree.