Most of the "alternative histories" about 1968 speculate on what would have happened if Robert Kennedy, after his victory speech in the California primary, had not entered the Ambassador Hotel kitchen where gunman Sirhan Sirhan awaited him. The original plan, according to advisor Jeff Greenfield, was for his brother-in-law Stephen Smith to meet him on the podium and take him in a different direction.
Based on my own research (post one and two), I have my doubts that Kennedy could have captured the Democratic nomination that year. It remains one of the great "what if's" of American history. One of the most persuasive essays suggesting that Kennedy would have won and gone on to become president is by Jeff Greenfield, in his book, "Then Everything Changed: Stunning Alternate Histories of American Politics: JFK, RFK, Carter, Ford, Reagan."
There's little doubt that if Robert Kennedy had lived, he would have made it easier for the Democratic Party to unify that year. The other defeated candidate for the nomination, Senator Eugene McCarthy, bitterly sat on his hands after losing. But RFK was much more of a team player. Vice President Hubert Humphrey lost to Richard Nixon by just 500,000 votes (43.4% to 42.7%). He was gaining on Nixon until the polls closed. Another day or two of a surge, and he probably would have won.
But it's unlikely either Humphrey or Robert Kennedy under any circumstances could have pushed back against long-term demographic trends, the rise of the Sunbelt and population shift of political power away from the old industrial northeast and toward the South. This trend became strongly apparent by 1976, cultimating in the elections of former Georgia governor Jimmy Carter in 1976 and former California governor Ronald Reagan in 1980.
Election analysts view 1968 as a realigning election: the "Solid South" left the Democratic Party for third party candidate George Wallace. Many Southern segregationists, raised as Democrats, supported Republican Barry Goldwater in 1964 because of his opposition to civil rights. They still considered themselves Democrats or "Dixiecrats" in 1968, supporting the local Democratic Party, but voted for Wallace for President. By 1972, Republicans had made enough enroads to began to win elections in the South. With the demise of old-guard Southern conservative Democrats, the GOP gradually became the majority party in many Southern states.