Amerigo Vespucci said:
More aggressive Soviet Union. Without an American effort to show how serious they were, and to tie down Soviet aid, the Soviet Union is more active worldwide. Possibly a conflict over Czechoslovakia in 1968.
Um...no and no. Soviet aggression in the 1970s, which was their largest expansion besides the immediate post-war era, was only possible because of the staggering loss of American prestige and confidence following Vietnam. Brezhnev, Kosygin (at first), and Andropov (as head of the KGB not his brief stint as General Secretary) were not the least bit intimidated by American willingness to throw away lives and treasure on a quagmire. If anything, they were hoping that America would continue to be stuck in other pointless bear traps.
As far as a conflict over Czechoslovakia, I have just three words
Hungary in 1956. Throw in East Germany in 1953 if you want. Americans were perfectly prepared to have the Soviets do as they wished among their captive people rather than risk a Third World War. In any event, the US was hardly likely to intervene on behalf of a country that offered no resistance to the occupation (they had good reasons not to, but the fact remains that Hungary resisted more than Czechoslovakia).
kitjed, Bulldawg, and Xen are probably right. I would suggest that the Democratic majority would continue without interruption or serious decline (though there would be a shift to the GOP in the South). RFK would likely be the successor to LBJ, although Humphrey can't be completely counted out. The northern ghetto riots would likely be less, though it's hard to say how much less.