At the risk of seeming to side with Rush Limbaugh, I am bemused by the controversy over the casting of Fred Armisen as Barack Obama in "Saturday Night Live”’s send-up of the contest between Obama and Sen. Hillary Rodham Clinton. The skit, which portrayed the media as star-struck Obamaniacs,  got more exposure than usual when Clinton mentioned it in the last Democratic debate. Hillary didn’t mention that the actor impersonating her rival wasn’t black. But others have pounced on  SNL’s decision to cast Armisen, who is of mixed South American and Asian ancestry, as Obama.

"Let's get one thing straight,” Hannah Pool wrote. “The moment anyone starts reaching for 'blackface,' they are on extremely dodgy territory. Anyone who thinks it's either necessary or, for that matter, remotely funny to black-up needs to have the gauge on their moral compass reset." But the point of Armisen’s impersonation wasn’t the mockery of the made-up minstrel; it was to try to create a reasonable facsimile of the senator. And it worked. Modern makeup is pretty amazing: It can make Joe Flaherty look like the late William F. Buckley Jr. and Dave Thomas a dead ringer for the dead Bob Hope. Physique and stature are harder to fake than skin color or Hope’s ski nose, which is why the lanky Armisen beat out his burly African castmate Kenan Thompson for the Obama gig.

So one response to the complaints about Armisen-as-Obama is that all that matters is the final illusion: Armisen may be a non-African-American, but he can convincingly play one on TV.  So why the controversy? I don’t think it’s because the impersonation is the moral equivalent of an old-style minstrel show, or because in casting Armisen as Obama Lorne Michaels was “taking sides” between Obama’s black and white parents or perpetuating the idea that Obama isn’t “really black.” The Washington Post offered another explanaton: the casting seemed to add insult to the injury of SNL’s chronic underuse of African-American performers. Here was an easy opportunity to feature a black comedian, and they blew it.

In this sense the Obama flap is reminiscent of another casting conmtretemps: the objection a decade and a half ago to the casting of the British actor Jonathan Pryce as an Eurasian pimp in “Miss Saigon” on Broadway. Pryce didn’t help matters when he said: ''If the character is half Asian and half European, you've got to drop down on one side of the fence or the other, and I'm choosing to drop down on the European side.''  (Armisen was wise enough not to make a similar comment about playing the biracial Obama.)  Actors Equity, which had refused to agree to Pryce’s casting, later negotiated a compromise with the producer under which he advertised for other roles in Asian-American newspapers.

That sort of outreach is a good idea, but it can’t resolve all the contradictions in the debate over race and casting which has been raging in theatrical circles, amateur and professional, for a long time. (I can be a source of strife in at schools where the racial composition doesn’t match the range of ethnicities in the school play.) Makeup can only do so much, and in some plays — a conventional  dramatization of “To Kill a Mockingbird,” say — it matters that the actor look like the character. But in others, the suspension of disbelief can be extended to accepting a black man in a part written for a white man  . . . or a short man playing a  tall man . . . or a woman  as Hamlet  (or John Travolta as a woman). But sometimes it’s too much of a stretch, as SNL will discover if it tries to cast Fred Armisen as Hillary.