Not sure Hatfield would be picked by Reagan for a running mate (Hatfield was probably one of the more liberal Republicans in the last 50 years; and even the fact he and Richard Nixon shared a mutual friend in Billy Graham wasn't enough to ensure he'd get the #2 slot in real life).
Maybe Ronald Reagan would have picked Richard Nixon as his running-mate in 1968, although Nixon might not be eligible to serve as Vice-President for another term. If not, either Gerald Ford, John Tower or Winthrop Rockefeller would have made decent choices as well.
Think I've seen an similar expression made elsewhere; but there's no question by 1968 Nixon wanted to be "the man". Can't picture him settling for the VP slot again (if he could at all).
As for the others: John Tower wouldn't be much more experienced nationally than Reagan was (being elected to the Senate in 1964). Gerald Ford's criticism of the Vietnam War as handled by LBJ -- not sure whether that would help or hurt his chances, and as for Winthrop Rockefeller; he became Arkansas governor the same year Reagan did (1966) and I'm not sure whether he was know for much beside being Nelson's brother.