The New Yorker has stepped in it this time. They think this cover is "satire." They say so.
The thing about satire is, it has to hit and hurt the intended target. It has to make the target scream in pain with the cruel unfairness of it (because it's true). The New Yorker cover doesn't do that. It doesn't even tell you who the target is. The magazine says the target is bad people who spread bad lies about Obama, but if you have to go explaining a joke, you probably shouldn't have told it.
Now, framing the target properly takes some study and reading of dirty nasty stuff that you won't find in the novels of John Cheever. National Lampoon was the best at it. National Lampoon's shit--from "Uncle Buckle the Safety Buffalo" ("Look out! Negroes!") to the Sunday Supplement of the newspaper parody ("Negroes--the Problem that Won't Go Away")--was funny. There was never any doubt for an instant who was getting his shit messed up, and it wasn't Negroes. It was middle-American white people who were getting their shit messed up. They were getting their shit messed up bad.
The New Yorker people probably never held an issue of the Lampoon in their hands. They also never listened to Lenny Bruce tell "how to relax colored people at parties." Lenny would carefully preface this routine with "This is a typical white person's concept of how to relax colored people at parties." (Yo! New Yorker people! Listen up!) Then he'd cue the piano cocktail music and he'd do the routine as dialogue , using one of the black people in his entourage as the straight man:
LB: Look, I'd like to have you over to the house, but there's a problem.
Black guy: What's that?
LB: I got a sister. [Pause] And I hear that you guys...[Laughter] Well, lemme put it to you this way. You wouldn't want no Jew doing it to your sister, would you? Well, I don't want no coon doing it to my sister.
At a guess, nobody there at The New Yorker ever heard this routine. They are too nice, too full of the earnest milk of uplift, too gentlemanly and ladylike and well-educated and well-dressed to bother with such stuff. They are also too nice to do what satire requires you to do, which is kick somebody in the crotch. Watching them try is sort of like watching your in-laws dance. It's cute until they fall and break a hip.