In an interview with Keith Olbermann, Barney Frank says that Obama will not defend Don't Ask Don't Tell if the repeal passes doesn't pass the Senate:

To give him credit, he’d been defending this is in court because presidents are supposed to defend laws. But he and I had spoken and some others: if, in fact, this had been filibustered — or if it still is, as I don’t expect it to be — then I believe he has no longer any obligation to defend it in court. If he’s against it, the House majority has voted against it and an overwhelming majority of the Senate votes against it, the administrators don’t want it — that’s lost its legitimacy and …he’s made that clear so yeah, the president was very helpful in this.

(UPDATED for derr.)