I wouldn’t care in any personal sense. There has never been and probably never will be a US president I personally care about because I’ve never known, and probably never will know, one enough to care about them. Not that I have to know someone personally in order to care about them; I cared about Michael Jackson without knowing him personally; but I have to think that the persona they’re presenting me with is generally real as opposed to generally fake. I also have to like them.
Most United States presidents, including Barack Obama, seem likeable enough. It’s just that I don’t think that’s really them. Being the president, at least in the United States, is a job in which being fake is basically a requirement. That fakeness mostly comes in the form of traditional formality and public diplomacy. If I had a problem with guys cheating on their wives, for example, I might’ve thought I liked Bill Clinton until the Monica Lewinsky scandal broke.
I would, however, care about Barack Obama being assassinated in the sense that I’d be intrigued with the whole thing as far as the details of how it happened and, to a lesser degree, public reaction goes. That’s why I generally like watching video documentaries and reading about presidents of the past; any important person, really; being assassinated. The fact that they’re held in such high regard and are so well-protected against it just intrigues me when it actually happens.