If that New Yorker cover has caused this much controversy, I think it's pretty safe to say that it failed at satire.
There's a number of reasons for that -- I think Chet nails most of it here, basically: it's hard for satire to keep up with the fevered delusions of the modern right. It's as if Swift had written A Modest Proposal at the same time as a number of London shops had just begun selling pies filled with mysteriously tender meat. What is the historical example of extraordinary satire would, in that context, be horrible.
Now, it's not the artist's fault that the right has been driven so mad over the Obamas, but great satire holds a mirror up to our culture and distorts it. The tragic thing for this satire -- which only a few months ago would have clearly been pitch-perfect -- is that at this point, there's no distortion involved.