I don't see any reason why he would have any better luck getting Medicare passed before the 1964 election than JFK did in OTL. If anything, because of his long record as a champion of civil rights, he might find it harder to get southern Democratic support for his legislative program.
Interesting. Guess it was really hard for Democrats to pass any worthwile legislation in the early 1960s. Maybe it was only the good economy and Cuba that made Kennedy's poll numbers rise.