It's not a matter of being an Obama supporter or of being surprised or offended by political satire or mockery of political candidates, as such. It goes in the category of
"With friends like this, who needs enemies?"

Had this cartoon been published on the cover of a right wing publication, I'd have shrugged it off as just another mag attacking someone on the other side. In fact, I think this same cartoon on the cover of The National Review might have been seen as so over-the-top inflammatory that it could have really worked to Obama's advantage.   The kinds of will insinuations, caricatures, and allegations that are spreading virally via right-wing blogs, emails, YouTubes, and trash radio talk shows would have had an important spotlight shone right on them -- making the "mainstream" media view it as a legitimate news topic.

But this cartoon was on the cover of what purports to be and is widely viewed as a "liberal" magazine. (One that is often picked up and browsed through by many far-from-liberal folks, I'd add, who just want to look at the cartoons and read the little newspaper bloopers inserts and wouldn't dream of actually READING the articles.)   

The cartoon itself clearly lampoons and caricatures the Obamas, NOT his opponents and their smear and gossip tactics, although the New Yorker editor maintains the target of the satire was intended to be the latter.
But the "intended target" of the satire is not depicted in the cartoon.   That's why, outside the context of the article it was supposed to illustrate, the cartoon does not come across as lampooning (and connecting negative images to) Barack and Michele Obama.