The current edition of Science (September 7, 2007- articles available only to subscribers online) contains a short article entitled “The Art of Virtual Persuasion.” The author notes a wide variety of studies that have shown that “people who mimic the gestures or speech of others are often perceived by those they mimic as more likable and influential.”
In this context Stanford University ran experiment one week before the 2004 presidential election. The volunteers were asked to fill out questionnaires regarding the two candidates (George W. Bush and Senator John Kerry) while viewing photographs of the men. One-third of the subjects were presented with photos of Mr. Bush that had been slightly (though not noticeably) merged with a photo of the experimental subject, making Bush look slightly more like the subject. Another third were exposed to a similarly altered face of John Kerry (doctored with the features of the subject). The subjects without strong partisan views “tended to endorse the candidate whose face had been morphed with their own.”
The article describes another experiment, from 2005, finding that students were more likely to agree with and unpopular proposal (that students carry an ID card at all times) when the animated character presenting this viewpoint looked more like the viewer.
Politicians have already picked up on this possibility for connecting with voters, “donning overalls for a meeting with farmers, then switching to a suit for a meeting with business executives.”
Psychologists like to say that "familiarity breeds fondness". So this phenomenon may or may not have to do with wanting a candidate who racially or culturally mirrors you- it could just have to do with the warm feeling of recognition we get when we see something familiar- like ourselves.