In no shape or form is the vaunted editorial page of The New York Times going to be let itself used as the president's trial balloon. You've got to be kidding me.
This implies a very straightforward "either the NYT is the POTUS's bitch, or it is independent" situation. I think there's a win-win outcome to be had, from the NYT's perspective, where the NYT prides itself on being the authoritative source that even the POTUS relies on.