I would brief the office of the President with the expectation that he would engage the Senate for an authorization to go to war based on the evidence of the imminent threat.
He wouldn't have got it nor would he have gone for it. The Generals were nervous because they were planning for the long term. With such a public pledge, the President could have authorised defensive measures to prevent Cuba getting to that state (eg increased intel, covert ops, etc)but a public invasion would have damaged US prestige and trustworthiness in the eyes of the world at a time when America needed to hold the west together.
Personally, I think there is much pride to be found in the fact that the idea was decisively rejected (Twice I think) by the office of the President. Coming up with the idea was understandable for the Generals - implementing it would have been a crime and no President would have done it (I believe).
Personally, I'd be worried if your generals weren't prepared to explore high-gain scenarios, no matter how distasteful. After all, your enemies always will.