Rachael,
I found your most recent post quite interesting. It is, I think, a good-faith effort to address an issue that has long bedevilled our politics. I offer this reply in the same spirit.
For starters, you seem to believe that an intellectual is someone who thinks he's smarter than everyone else. (Thus your decision to treat "intellectual" and "elite" as synonyms.) Certainly there are intellectuals who believe this, though experience has taught me there are quite a few non-intellectuals who believe the same thing about themselves. More to the point, I think this imputation takes us away from the common usage of the word and introduces important confusions into the argument. Surely "intellectual," in everyday speech, simply describes a person with a passionate devotion to ideas--- someone who values them for their own sake and puts them at the center of his or her life. Now anyone who genuinely engages with ideas knows how resistant they are, how truly difficult it is to work through the logic of anything complex enough to be worth thinking about. Real intellectual effort should, and usually does, make for humility, not arrogance. Socrates was right: the more you know, the more impressed you are by all the things you don't know. It follows that those too "consumed by everyday concerns" to snuggle up with Principia Mathematica are not properly described as anti-intellectuals. They are simply people who have devoted their lives to other things. This doesn't make them hostile to ideas, any more than a classical pianist has to be hostile to baseball.
Why, then, is there suspicion on the part of so many--- a suspicion exploited by certain politicians, mainly on the right--- that "intellectuals" look down on them and constitute some kind of cultural fifth column? I think there are mainly two reasons. The first is the genuine differences between intellectuals and non-intellectuals in modes of life, in habits and behavior. Intellectuals spend a lot of time reading long, abstruse books, then sit around thinking about what they read. They may write about it, too. And they put a premium on discussion and debate--- on exposing their beliefs to the criticism of others. These are all things that non-intellectuals devote relatively less time to. In a country such as ours, where ethnic, racial, and religious diversity are so pervasive, these kinds of cultural signifiers are importantly connected with basic questions of identity.
The second consideration is this: many intellectuals see their form of life as largely optional in most cases--- as a matter of personal inclination or interest. Reading, argument, and reflection are great if they turn you on, but most of life can be gainfully navigated without them. It remains true, however, that in certain subjects these practices greatly enhance our ability to form reliable views. The sciences are the most obvious example, but many intellectuals would insist that politics belongs here as well. In other words, they would argue that getting our ideas right is an important part of getting our politics right. This doesn't mean that any intellectual, right now, has the right ideas, and it certainly doesn't mean that non-intellectuals lack worthwhile ideas. But it does mean that intellectuals are inclined to be sceptical of political notions that are obviously ingenuous or unconsidered. And this makes for a certain tension.
I've said that intellectuals are persons with a certain connection to ideas, and that most non-intellectuals are not anti-intellectuals. What, then, is anti-intellectualism? Well, given our definition above, an anti-intellectual is someone who explicitly rejects the value of ideas and critical thought--- someone who thinks a life built around these things is simply quixotic, absurd. Such persons will also reject the notion that getting ideas right is essential to getting other things right--- politics, for example. They will not emphasize, or even accept, the value of testing our beliefs against the opposing views of others. They will tend to think that beliefs are justified in other ways--- through instinct or intuition or insight, or through a steadfast confidence in a particular vision of the world. Faith, in other words--- whether ideological or religious.
It is this constellation of attitudes that Bush and Palin so obviously share. So, apparently, does a significant, if strictly delimited, number of their supporters. We know that Bush lives in a bubble of certitude, that he is impatient with argument and dissent, that he sees doubt as weakness and nuance as confusion. We know that his political life is as faith-based as his spiritual life. From every visible evidence, the same is true of Palin. This is why we are justified in describing them as "anti-intellectuals," and why so many people, intellectuals and non-intellectuals alike, are properly terrified at the prospect of another presidency infected by this delusion.