This is a big change--no USSR.
The USSR was essentially considered the "bad guy" in the West, both by the leaders and by most of the people. Many Western politicians were succesful by playing off of the people's fears of the USSR and Communism. Without those fears, these politicians would not have been so succesful. As someone pointed out above, Hitler is one example of a politician who came to power largely due to voters' fears of the USSR. Without a USSR for people to be afraid of, Hitler would not have come to power.
The existence of the USSR created a rift in the global socialist/Marxist movement. Marxists had to decide whether they were allied with the Soviet Union or not. In most countries, the socialists split into two or more parties, usually the party supporting the USSR were called "Communists" while the party that did not support the USSR were called "Socialists". Without the USSR, these splits would not have taken place, and so the Socialist movement would have been more united, therefore more powerful, in Western Europe and in the United States.
The presence of the USSR gave opponents of socialism something to point to and say "that's what socialism is, you don't want that!" Without the USSR to discredit it, many people who in OTL were turned away from socialism might instead be attracted to it. This again would strengthen socialism, giving it more support and more voters. I don't think a socialist president of the United States is completely out of the question in such a timeline.
No USSR means no cold war, which means no arms race, and no space race. We probably do not land a man on the moon by 1969.
Just some thoughts off the top of my head.
KEVP