So Johnson would have to maintain support in all Democratic states that didn’t go to Wallace IOTL and just convince one more to back him to win?
That’s not a cakewalk, and would really damage his popularity, but it’s well within reach.
No; he'd need to get two more states to back him to get a majority; i.e., 26 of 50 state delegations. Thus, he'd have to secure party loyalty in any two of the Wallace states.
I should have realized that
if the election went into the House, it would be Johnson's to lose, given the breakdown of state delegations--at least on the surface. But he has to convince at least two states that might potentially bolt to hold the party line. And that won't be easy without the bargain. (I'm not sure what happens to the split states: I suppose they vote "present" but don't cast a vote for a candidate since in all likelihood there would be no agreement.)
From what I can see, Johnson's best shot at gaining a Wallace state would be Arkansas: that was the one in which Wallace's victory was closest. It's tough to guess how much influence Wallace might have on the congressional delegation in any one state, or where the representatives place the greater priority: the popular vote outcome or party loyalty. If it's the former, Lyndon Johnson would have to make a Faustian bargain with Wallace. That would pretty much make his victory hollow, particularly in the north, and with minorities.
The term from 1969 to 1973 will be incredibly turbulent, and I suspect Johnson might not survive. But either way, the Dems are doomed in 1972. Either Humphrey or whomever would get the nod would have several tons of Johnson baggage, starting with the Wallace bargain. All the GOP has to do is nominate a reasonably moderate candidate (Nixon would be finished; Rockefeller still has baggage from his divorce) and they're home free. Someone like Charles Percy or Howard Baker would work admirably.
Footnote: Spiro Agnew would be no more than a political footnote / joke, and the headlines for his corruption indictment would probably go no farther than the circulation of the Baltimore newspapers.