Before convention or election.
As the 50s had been relatively hushed up it would seem that he would have lost both, either Adlai Stevenson or Lyndon b Johnson win the convention or Nixon wins the election, either way I can see a withdrawal from Vietnam occurring faster and/or the creation of a dystopia for progressives or utopia for conservatives. No major anti-war protest means no sexual revolution, and while the black rights movement would have ended in success we would see no native Americans rights, feminist women's rights, or war on drugs.
In other words birth control and abortion would be looked down upon, the anti-catholic sentiment of the USA would still exist, but on the other sides blacks may be more successful and perhaps better economy?