Eisenhower looks better for one change.
President Kennedy, Johnson, Humphrey, or McCormack decides not to send large scale assistance to the South Vietnamese governnment and by the Spring of 1968 Ho Chi MInh has all of the country.
How big of an issue do the Republicans make of it?
How well would it play with voters?
With no Kennedy build up of advisers - 700 to 12,000 during his Presidency - you have their numbers limited to what Eisenhower set it to. My understanding - and it is only from one source, so can I get a confirm or deny from someone - is that Ike deliberately kept the number of advisers down to what would fit into the evacuation ship that he kept in Saigon harbor fueled, provisioned and ready to go on twenty four hours notice at all times.
If this understanding is correct than Ike clearly understood that this was always likely, and the US President of the time could sell the idea that 'well we were never committed to fight for the place were we?' and go on to try to rally the non-communist neighbours. It would not be seen as an American defeat, which would limit interest from much of the press and politicians from countries outside south-east Asia.
Maybe a million Vietnamese, 60,000 Americans, as well as many South Korean, Australian and New Zealand men get to grow up and live lives and that will have some kind of unpredictable effect. The Counter-culture youth movement loses one of the drivers for it's rebellious attitude, how much this would take the edge off is anyone's guess. Possibly not too much, the baby boom generation is still going to be rejecting their parents.
Without so many veterans coming home with drug habits and the CIA funding its war in Laos with the stuff does the drug culture stay the smaller problem of the 50's? What effect does that have, what will the people who otherwise got involved in that do with their lives instead?
Of course the fall of the Republic of Vietnam could go unnoticed because Kennedy decided to send all those advisors somewhere else. The big US war of the 60's then happens in Lebanon or something, there is actually a good David Drake novel with that background. It ends with a Lebanon war veteran retaking the orbiting US nuclear missile base from Nazi's who stormed the place with Kurdish shock troops.
At a guess that is probably not going to be happening...