Upvote:5
I think you are being misdirected by the theatre of politics.
It works like this.
Somebody does something "against" the leader.
The underlings and sycophants make a noise about it, as they must.
The leader takes it in their stride, rises above and appears more statesman-like.
So, from my recollection, the answer is that it had a positive effect on Kennedy's image.
Set in the context of the Cold War, it was a blow against the totalitarian governments. It was a statement of the strength of democracy:
Look, people are free to mock the President. The President enjoyed the joke too. And the guy is still alive!
It became part of the tapestry of propaganda by which people "in the east" could potentially be influenced.
I'm not suggesting that this album made it past the wall, or that it was planned as a weapon. Just that Kennedy's response fits the pattern of the times.