It obviously was an attempt at satire, but it fails. It represents the basic stuff that you get from the Right about Obama, but it neither mocks nor exaggerates them. It's a sad state of affairs that conservatives are hard to satirize or parody because they're so insane, but that's where we are. The only context is that it's on the cover of the New Yorker and Everybody Knows That They're Good Liberals So It's Satire. But, look, whatever the merits of the New Yorker it's more "elite chattering classes of New York" than "good liberal." Not quite the same thing, even if there's some overlap.
The upper-west-side elites at the New Yorker undoubtedly assumed that cover would be taken as satire. Although if it wasn't, they probably didn't care that much. The result was a lazy, tin-eared piece of work indistinguishable from what the fear-of-an-Obama-planet folks on the right would eagerly say without a hint of irony. (Scroll down here to the quote from "Doughy Pantload" aka right-wing legacy Jonah Goldberg of the National Review Online.)
Can't un-ring the bell on this one; it's out there and that's that. And frankly, even in the hands of the fear-Obama folks, it's not as bad as much of what we have heard and will continue to hear from them during the campaign, to say nothing of what will be casually piled on by the "mainstream media." So barring something amazing and unforeseen, this is the last time p3 will need to cover that cover.