What the editors at the Poor Man Institute say: http://thepoorman.net/2008/07/14/liberal-blogosphere-death-spiral-watch/
The New Yorker is a sophisticated publication, and its readers know satire when they see it. Dumbasses who really believe, or who might even be persuaded to believe, that the Obamas are Muslim extremists don't read the New Yorker. Except maybe to take all the cartoons, cover up the captions, and substitute "f**k you" in all of them.
Sure, the cover will be shown on the cable news networks, especially the pretend news channel at FOX, but FOX viewers won't get it, and it will have to be explained to them. Anyway, FOX viewers aren't going to vote for Obama anyway. CNN probably won't suggest that the cover is truthful except as satire, assuming that annyone at CNN knows what satire is.
New Yorker is not an organ of the Obama campaign or the Democratic Party, so its editorial decisions are probably not based on political considerations as much as some liberal bloggers might like.