That would be hard because there's just too much for splitting to really work. In Mississippi, Goldwater beat Johnson by 75%, 87%-12%. That's huge. Even in my scenario, that's still Goldwater at 77% and Johnson at just 22%. Cleave Goldwater's vote cleanly in half and both sides would beat Johnson by 16%. Even with an even three way split of Goldwater's vote, the three factions would beat Johnson by three percent. As for Alabama, Goldwater did worse than Mississippi, with just 69% of the vote OTL, but on the other hand, Johnson got zero votes (with the remaining votes going to an unpledged Democratic ticket)Ive always been facinated by the idea of a 50-state-landslide for LBJ in 1964, but I dont dont know how that would come about. Maybe a last minute well organized dixiecrat campaign splits the vote in th deep south?
Well, actually, I do think it could be done. Let's say that the Civil Rights Act of 1964 goes further than OTL, maybe contains elements of the Voting Rights Act of 1965 and maybe more. Whatever it is, it is enough to provoke Mississippi and Alabama to secede, starting another civil war. Except it's extremely one sided compared to the first civil war, just consisting of those two states declaring secession and then quickly getting crushed. But it occurs shortly the election (and also in this scenario, let's say Johnson is able to at least get himself on the ballot somehow in Alabama too). The Johnson Administration declares that the election will still be held in those states, in areas that are controlled by the US on election day, the Federal advance into the states starts from the black belt areas and fans out from there, and by election day the Feds largely just have black majority areas under their control (and with all the military/law enforcement presence in the area, they are able to prevent voter suppression of the black vote)
Apart from an extreme scenario like that though (which already stretches plausibility), I have a hard time seeing Johnson overcome those huge Goldwater margins in Alabama and Mississippi, even with some split to the Goldwater vote
...maybe there is another alternative though. Change up the GOP primaries/convention, and give Rockefeller the nomination. He still likely does poorly vs Johnson, but could potentially be rather more competitive than Goldwater. Problem is, he was a pro civil rights Republican. So he's potentially even worse than Johnson (who at least was a Democrat and from the South) to southerners. So maybe under those conditions, you could have a situation where the south ends up more of a three way between the GOP, national Dems, and Dixiecrats, where Johnson could manage to just barely win all of them? And as for Rockefeller being stronger outside the south, maybe his divorce and remarriage, which upset conservatives OTL, leads to a weakening of support among the right that helps allow Johnson to win everything. Hell, maybe it could help basically have a Wallace '68 style run 4 years earlier, with Wallace being the Dixiecrat and running outside the south too as the conservative oriented candidate to help cut right-wing support from Rockefeller enough to deny him any states outside the south. Or something vaguely along those lines