I'd bet fewer than 25% of American adults can tell you both of those things.

Plain and simple:

Obama got elected because he is a great speaker and he's charismatic. Qualities much closer to being a popular actor or religious figure got him elected rather than his intellect.

It didn't hurt that people were tired of the previous party (this is a common pattern).

A JD is not a research degree. It is a second entry degree, meaning there is no necessary reason it could not be an ordinary bachelor's degree. A JSD is the US Law School equivalent to a real doctorate.

Obama was the first President of the HLS in yeeears not to publish. He's a very, very smart man but calling him an intellectual might be pushing it. His popular works are not brimming with ideas.

Don't forget that 46% of the country still voted for John McCain - a person was extremely terrible academically even after the Republican Party had launched two disastrous wars, exploded the deficit and their lack of regulation and oversight had caused the worst recession since the Great Depression. And as others have pointed out, Obama wasn't really elected because of his intellectual ability but because of the state of the economy at the time and because he's a charismatic speaker.