In an October 2, 1963 National Security Meeting where the McNamara/Taylor report was discussed, JFK expressed "reservations" about the proposed 1000 troop withdrawal by the end of the year.
Here is the exchange with McNamara.
President Kennedy: My only reservation about it [the report] is that it commits us to a kind of a ... if the war doesn't continue to go well, it'll look like we were overly optimistic, and I don't—I'm not sure we—I'd like to know what benefit we get out [of it] at this time announcing a thousand—
McNamara: Mr. President, we have the thousand split by units, so that if the war doesn't go well, we can say these thousand would not have influenced the course of action.
President Kennedy: And the advantage of taking them out—
McNamara: And the advantage of taking them out is that we can say to Congress and people that we do have a plan for reducing the exposure of U.S. combat personnel to the guerrilla actions in South Vietnam—actions that the people of South Vietnam should gradually develop a capability to suppress themselves. And I think this will be of great value to us in meeting the very strong views of Senator [J. William] Fulbright and others that we're bogged down in Asia and will be there for decades.
President Kennedy: All right.
That's not much of a disagreement or reservation to me; it sounds half-hearted and staged. And completely political. JFK wanted McNamara to give him cover, cover for something he didn't want attributed to him.
You can hear JFK himself say this in a taped recording of that meeting:
https://www.jfklibrary.org/asset-viewer/archives/jfkpof-mtg-114-a49dGo to the 19:00 minute mark.