Robert Kennedy's biggest problem in 1968 would have been winning the nomination, not the general election. I think Fulbright would have been his most likely v.p. pick.
Two problems with your VP selection.
- Fulbright himself was up for reelection in 1968 and it's quite possible he'd rather opt to secure another term rather than risk everything, including considerable seniority in the Senate, in an uncertain presidential race.
- His vote against the 1964 Civil Rights Act would make Fulbright's nomination very difficult.
