“Authoritarianism” is a personality characteristic that political psychologists use (among many others) to explain political attitudes and voting behavior. To clarify, when political psychologists say that someone is ”authoritarian”, they do NOT mean that he or she is a fan of authoritarian dictators, fascists, or Nazis. Rather, it means that the person has a high need for order. Authoritarians are motivated to seek “clarity in the face of confusion” (i.e. they don’t like nuance or ambiguity) and they tend to “rely on established authorities to provide that order” (Hetherington and Weiler 2009, pg. 34). In other words, authoritarians see the world in terms of “black and white” rather than “shades of gray”, and they feel comfortable submitting to authorities who provide a black and white understanding of the world, be they political, social, or religious leaders.
In current American politics, authoritarians tend to be conservative and Republican, although authoritarianism is not the same as political conservatism (it’s related to social conservatism, but not necessarily economic conservatism). There are also many authoritarian liberals and authoritarian Democrats, although they are not as common as authoritarian conservatives and Republicans (Hetherington and Weiler 2009, ch. 5). A black and white worldview simply lends itself better to Republican positions on foreign policy, civil rights, etc.
Here is a break-down of levels of authoritarianism in 2008 Republican primary voters vs. Democratic primary voters (data from the 2008 ANES):
LEVELS OF AUTHORITARIANISM AMONG 2008 REPUBLICAN PRIMARY VOTERS:

LEVELS OF AUTHORITARIANISM AMONG 2008 DEMOCRATIC PRIMARY VOTERS:

Again, we see that authoritarianism is common among both Republican and Democratic primary voters, but is more heavily skewed toward the high end among the Republican base.
To me, all this spells trouble for newly-announced candidate Jon Huntsman. Of all the declared GOP candidates, Huntsman is perhaps the most “nuanced” in his personal background and policy positions. He’s the former governor of one of the most Republican states in the country who accepted a job working for a Democratic president as ambassador to a country with a non-Western culture. He’s a political conservative who is pro-immigration and pro-civil unions. He’s a former missionary for the LDS church, but says “I get satisfaction from many different types of religions and philosophies.” All of these nuances scream “shades of gray” rather than “black and white”. This may well end up being his greatest difficulty to overcome as he seeks to win support of the Republican primary constituency in 2012.