POD is Humphrey's cancer is treated early enough to at least buy him a few years of 'good' health'. I'm not going to try to butterfly away an early death for him, because that's too close to ASB, but the main question doesn't work if he's near-death. So let's say, Humphrey's at least expected to be able to survive until 1980 or so, even if incorrectly... or he decides simply to run for president anyway, if you can't buy cancer remission.
Humphrey announces he'll run for the Democratic presidential nomination in 1976. How does the field change? Who is his running mate? Does he perform better or worse than Carter? Is he more or less effective? If his cancer resurges while he's in office, how do people react? If terminally ill, does he resign early, or stay in office his final months? What does 1980 look like if he wins? What is his legacy? Etc. etc. etc.
Humphrey announces he'll run for the Democratic presidential nomination in 1976. How does the field change? Who is his running mate? Does he perform better or worse than Carter? Is he more or less effective? If his cancer resurges while he's in office, how do people react? If terminally ill, does he resign early, or stay in office his final months? What does 1980 look like if he wins? What is his legacy? Etc. etc. etc.