Is it possible hadn't there been a big expensive US involvement in Vietnam. That LBJs great society could have given National Healthcare? If that had happened how would America have looked today?
Canada started its Medicare roughly in the mid-60's (each province opened at a different time). That country was unburdened by war. Yet, it has a smaller population and a much different political makeup than the US.
I don't think that single-payer American Medicare would have passed even if Vietnam were butterflied away. Maybe something like Obama is proposing might have passed, especially if there were no public option. The managed-care insurance models found in the US today were not around in the 60's, so it's hard to make a comparison between LBJ Medicare and the Obama plan.
There would be great opposition from fiscal Republicans over a universal single-payer, and I suspect there would be protests similar in tenor to the ones that are seen today over the current health-bill. Remember the Cold War and the "democracy vs. communism" dichotomy loomed large in the American consciousness (i.e. McCarthyism). Butterflying Vietnam away would not likely change this political dichotomy. UHC would appear 'socialist' (as Lazar below notes about public perception of Truman's UHC plan.)
Some Americans to this day consider the Great Society a high water mark of Democratic spending and statism, and consider that time in history a low mark for the American government. What we see today with Obama and his plan has antecedents in LBJ and the general ethos of American politics.