The Presidential Timber test is one that I emphasize because it's easy to drop Obama into a certain point in the timeline and say, well, sure, all he had to do was beat Hillary and McCain, anybody could have done that. No, the Presidential Timber test is: Would it occurred to many people a couple of years before the election that this person sounds like a plausible winner and plausible President?
But if there had already been a first black President, if that box had been checked off in American history, what of Obama? My guess is that in that alternative history, he would be a nonentity.
Obama generally has not struck people who knew him well as a natural leader in smaller scale organizations, and his performance in positions like chairman of the Annenberg Chicago challenge did little to change minds. It was always First Black President or Bust for Obama.
By the way, if, say, George Romney had become the first Mormon president in 1968 or Mo Udall had become the first Mormon President in 1976, I could well imagine Mitt Romney not running for President. I have this theory that Romney keeps running for President because he secretly wants to be the Mormon JFK who normalizes his people by becoming President.
But I can't imagine a Udall Presidency would have had much effect on whether other people would have considered Mitt Romney to be Presidential Timber. The number of non-Mormons in America who feel deep down that it's time to elect a Mormon President, even if he isn't particularly qualified, are minuscule.