In OTL McGovern was seen as unable to run because his Senate seat was up in that year. Suppose that had not been the case.
I think that both the 'Bobby' and 'Gene' wings would have supported him.
It would have been pretty clear that he had a moral right to the Democrat nomination.
LBJ's control of the machine might have denied him the actual nomination.
That, along with other events in Chicago, might have caused a massive walk out.
As I understand it US opinion was divided on the wisdom of the war.
Given a first past the post voting system and 3 pro war candidates against one anti war one well.....