The conclusion? This solves nothing. And the fact that our President felt the need to subject himself to this means we all lose.
Update: I really appreciated the words of David Frum on this matter:
[T]hose who imagine that they somehow enhance the value of [American] citizenship by belittling the American-ness of their president – they not only disgrace the politics they uphold, but they do damage that will not soon be forgotten by the voters a revived Republicanism must win.
Salon also has some arguments on why this wasn't Obama caving; it was Obama cannily portraying the Republican party as out of touch and a tiny bit crazy.