Despite the often understated importance of Ambassadors in guiding US foreign policy, I doubt even a magician like Clifford would have really turned it around. Kennedy did try fairly hard IIRC with India, but he was running up against fundamentals in Indian foreign policy at the time. The best reaction he got was the border clash with the PRC in 1962, but once that had passed India just reverted back to Non-Alignment, albeit with cordial relations. And that was with a massive foreign aid program, sophisticated arms supply to the Indian military, and Kennedy's commitment to defend India against external attack if it really came down to it.
To really drive home the necessity of closer relations with the US, IMO there has to be a sustained danger, either external or internal, from those damned Commies.