Had Nixon done so sometime in 1972--that is, gone on TV with a public acknowledgement and apology, coupled with throwing Haldeman, Ehrlichman, and a few others under the train--he still would have won by a landslide. (OK, he might not have carried Rhode Island, Hawaii, and a few other states that went Republican in that aberrant year but still...)
Chances are most of what the fired staffers had to say in terms of accusations would have been brushed aside as coming from disgruntled former employees, at least in the short term. As I recall, Ehrlichman and Haldeman both died in the late '80s: at that point, one suspects that a lot more dirt might have surfaced. Nixon's historical stock would have fallen, but one suspects that would have been temporary: he would have had his reputation ameliorated with the end of the cold war/fall of the Soviet Union assuming that happened as it did in OTL, given that he was a consummate cold warrior in his own right. (One can almost see an interview with Nixon on CNN on that night in 1989 when citizens were taking sledgehammers to the Berlin Wall.)
In summary, Nixon would probably be recalled today as an above-average president, given that he opened relations with China and (projecting) ended the Viet Nam war. Watergate would be viewed in the US as the less savory part of his character shining through, mitigated by his apology; abroad, that would be shrugged off as business as usual.