Scott Walker, an all-but-declared candidate for the Republican presidential nomination, didn't graduate from college. That's unusual--as far as I know, the last "major" candidate for president without a college degree was Paul Simon, who sought the Democratic nomination in 1988. Ted Cruz, a declared candidate for the Republican presidential nomination, got an undergraduate degree from Princeton and a law degree from Harvard. That's not unusual--George W Bush had degrees from Yale and Harvard. But most Republicans with degrees from elite schools have downplayed them--Bush talked about Midland, Texas, a lot more than he did about Harvard or Yale-- while Cruz has made them a central part of his story.
Do voters care about this sort of thing? A 2007 Pew survey asked respondents if they would be more or less likely to vote for a candidate with various characteristics. One was "attended a prestigious university such as Harvard or Yale," and another was "did not attend college." People were split on a candidate who hadn't attended college: 49% said it would make no difference and 47% said they'd be less likely to support the candidate (only 3% said they would be more likely to). Most people (74%) said that attending a prestigious college wouldn't make any difference; 20% said more likely and only 5% less likely.
A common perception is that liberals value educational credentials, while conservatives are less interested, or maybe even hostile. In fact, that was why I started thinking about the issue: would Cruz's association with elite colleges hurt him with "the base"? According to these questions, there might be some difference in the expected direction, but it's small, Another potential influence is education: you could make arguments for an effect in either direction. It turns out that, less educated people may be a little more likely to say that not attending college wouldn't matter; education has no clear effect on views about having attended a prestigious university.
I had no reason to expect gender to make any difference, but since nothing very interesting was going on, why not try? Gender didn't make much difference for reaction to a candidate who hadn't attended college, but made a substantial difference for reactions to one who attended a prestigious university: 8% of men, and only 2% of women, said they would be less likely to support one. To put it another way, more than three-quarters (60 out of 79) of the people who said they would be less likely to support the candidate were men.
Even among men, attending a prestigious university was much more likely to be a plus than a minus, but the gender difference needs an explanation. My thought is that a "man of action, not words" image has appeal to some men, and there's no real parallel to that image for women.
[data from the Roper Center for Public Opinion Research]