The vast majority of the people who will see the cover of the New Yorker magazine will not think too deeply about it. They will glance at the cartoon, which will generate an instant emotional reaction. They will then attach that emotion to Barak Obama and, over the next four months, interpret further information through the lens that this cartoon generated.
This instant, unreflective, shallow interpretation of the cartoon for a lot of people will be the idea that the Michelle and Barak Obama hold pro-terrorist/anti-American sympathies who are trying to gain control of the White House. The cartoon ends up reinforcing the very ideas that the author intended to ridicule.