I'm of the mind that Kennedy would have appealed more to both the white working class and the new left than Humphrey did. If I had to predict an electoral result, it would be something along these lines:
Robert F. Kennedy/Terry Sanford (D): 43% of the PV, 271 EVs
Richard Nixon/Spiro Agnew (R): 42% of the PV, 211 EVs
George Wallace/Curtis LeMay (AI): 15% of the PV, 56 EVs
The race comes down to three states: California, Illinois, and Ohio. I think Kennedy wins all three. California because of his superior support among Latinos and African-Americans, as well as the Democratic Party's organization in that state (Jesse Unruh) being more strongly aligned with him than with HHH. Illinois because Kennedy wins over more ethnic Catholics in Cook County, and Ohio because he is better with white working class voters than Humphrey.
Truman's three saving states in 1948 would be what saves RFK in 1968, but I'm not convinced that he can stand up to the Nixon machine. Towards the end, Nixon got complacent campaigning against Humphrey because he had such a wide lead. Nixon would throw everything plus the kitchen sink at a Kennedy, plus more. He wouldn't let his guard up for a minute.
Unruh did jack-all to help HHH in 1968, but his backing of RFK isn't all a rose story:
I do think that the California race would be a closer one, but no cigar. Nixon has people in his state, too.Willie Brown: A Biography said:Contrary to post-assassination myths, the Kennedy campaign in California was chaotic and disorganized. Unruh and the California politicians clashed with each other and with the East Coast consultants Kennedy sent to the state to straighten things out. Unruh tried to manage every detail, and details began to escape him. Kennedy almost did not get on the California ballot because lawyers dispatched by Unruh to the secretary of state's office barely made it before closing. Meanwhile, the Kennedy staff treated the Californians brusquely, and tensions grew. Well-meaning volunteers were haughtily turned away from the campaign organization. Finally, Kennedy sent campaign aide Steve Smith to California, and he set up an office next to Unruh's. Everything in the campaign from then on had to go through both Unruh and Smith for approval.
Finally, it is true that Kennedy did better than Humphrey among the white working class in 1968. McGovern also did better than Humphrey among this "Wallace crowd" in 1972, most notably in Wisconsin. I expect Nixon to do his best to pry this group from Kennedy, like he did from McGovern IOTL. And I think this would be enough to defeat RFK. This group would later be known as Reagan Democrats for a reason.
If you are going to get an RFK presidency, though, that map is the most plausible pathway I see.