We'll never know for sure what might have happened. I personally subscribe to civil rights role as being what cost him the most. Clearly the friction at home between growing race-based insurgency and the perspective that Vietnam was yet one more example of African Americans bearing an unfair brunt of the fight there merged in the protests at home. Between the two he was finished, and from what I have seen and read it was the blowback to his work on civil rights that drove his rapid decline after leaving office.