Isn't that the point of irony? It's not about getting someone to say, "Hey, I get it. That's clever." It's about getting people to come face-to-face with absurdity. It expresses the truth in the guise of a lie. The image is false and offensive, but in showing that, it has exposed a lot more about bigotry underlying attacks on the Obamas than a direct refutation may have. Lakoff writes about how simply denying a claim ("Obama is not a jihadist") can reinforce the idea that you're trying to attack.
Then again, irony can do the same thing (see the people who are cynically ironic and use their detachment to get away with offensive rhetoric, or to paraphrase Zizek, those who know that what they are doing is wrong and are doing it anyway). There is the risk that the image will be adopted by those who actually believe Obama is a secret Muslim. A number of conservative editorial cartoonists have attempted to do this, identifying Obama with those that protested the Danish Mohammed, even though his comments have been very reasonable:
"I know it was The New Yorker's attempt at satire. I don't think theyYou can see what passes for conservative humor: here, here, and here.
were entirely successful with it," Obama said. "But you know what?
It's a cartoon ... and that's why we've got the First Amendment."
So some people have taken this as a chance to express horrible views under the guise of irony.
But the people who spilled the most bile over the cartoon were the same ones who propagated the lies that it depicts in the first place. It's telling that someone like Bill O'Reilly was offended by it. Sometimes the subversive move isn't to disidentify with an oppressive image, but to overidentify with it. The cartoon got too close to the racism underlying American politics and people recoiled in horror from it, in the same fashion that the Cathar heresy was offensive to the Catholic church because it came too close to Catholic ideology and demonstrated its inherent excess.
The whisper campaign against Obama has operated by staying under the radar. The GOP benefits from rumors that are spread via dispersed networks, such as e-mail, but can't directly propagate them for fear of being exposed for encouraging bigotry. The cartoon provokes anxiety because it threatens that distance.
Maybe it wasn't entirely successful, but I'm not sure that the case is as simple as people are making it out to be.
Edit: Let's watch idiot cartoonists run this shit into the ground!