RFK Effort Falls Short at the Convention
While I like RFK and his tragic 1968 campaign makes for a great What-If scenario, I doubt he would have won the Democratic nomination that year. The RFK legend that has grown since 1968 exaggerates his popularity at that time, overlooks the problems of his late-starting candidacy, and underestimates the determination of his opponents.
Even after learning that he had won both the California and South Dakota primaries on the night of June 4, 1968, RFK reportedly stated that his chances of winning the nomination were still no better than 50-50. Vice-President Humphrey was ahead by approximately 500 delegates at that point.
LBJ, who controlled the DNC prty machinery, would have done everything in his power to stop RFK from winning the nomination over Humphrey. Corporate money poured into Humphrey's campaign coffers because of business opposition to RFK. Humphrey had Big Labor and the southern Democrats supporting him as well.
Senator Eugene McCarthy deeply resented RFK jumping into the Democratic presidential race in mid-March and stealing McCarthy's thunder, after RFK declined the opportunity to run against LBJ as the sole anti-war candidate back in the autumn of 1967. McCarthy would have contested the June 18th New York primary and cost RFK two valuable weeks campaigning in his home state, while Humphrey worked the non-primary states for delegates. McCarthy stated that he would not have stepped aside in favor of RFK at the convention, so McCarthy's own 200+ anti-war delegates would have been denied to RFK on the first ballot at least. McCarthy preferred Humphrey over RFK. In short, the anti-war and anti-Administration camp would remain split between RFK and McCarthy--which benefitted Humphrey.
As in the What If? written in 1982 by UC Berkley Political Science Professor Nelson Polsby (who began teaching at Berkley in 1967), I think that RFK would have come up short in his efforts to block a 1st-ballot nomination of Humphrey. A victorious Humphrey may have offered RFK the vice-presidential spot on the Democratic ticket (as he did to Ted Kennedy in OTL), but RFK would probably have declined given the defeat of the anti-war plank to the Democratic Party platform at the Convention. A Humphrey loss to Nixon would have cleared the field for RFK to run for the Democratic nomination in 1972, which was the original plan before Tet in early 1968 and McCarthy's strong showing in the New Hampshire primary convinced RFK to run that year.