I agree. If Strom Thurmond fighting against "Desegregate the Army" Harry Truman could only take 4 states in 1948, I doubt that Cactus Jack could sweep most of the Solid South, or even put his home state of Texas in danger of being lost. He might be able to take 1 or 2 states, or get some faithless electors like Harry Byrd did in 1960, but no way he could win that much.
The difference here is that we have a much wider swathe of issues being disputed beyond Desegregation, and that the candidate in question is the sitting Vice President, not the newly elected Governor of Southern Carolina. If we are talking about a real break here then much of the Conservative Coalition is going to come out and endorse Garner for the Presidency, and that would include more than a few party machines down South. Those states are liable to remain with Garner as he would, as Thurmond was, be labeled the Democratic nominee in those states, though in my opinion I would swap Oklahoma and Florida.
Now, Garner is not going to be running as anything other than a Democrat, or some variation of it (National Democratic, Conservative Democratic, Conservative, Stetson Democratic, etc.), and he won't leave the party; his break is with Roosevelt and the Progressive wing, not the Democratic party as a whole. However that still leaves the House a mess considering the situation there.
Roosevelt is going to win the popular vote, no question; Garner is going to be pulling votes from Willkie just as he is going to pull votes from Roosevelt, so I don't see the margin between the two dropping all that much except when the South is factored in. Even with that backdrop however Roosevelt is going to be short of the required number in the House to win due to Garner, and the Republicans aren't going to budge putting a few other states out of contention as ties. What might eventually happen is either Garner backs out and directs his support to Willkie, allowing him to be elected to the Presidency as a compromise choice, being the middle field between Roosevelt and Garner. I could also see Garner being selected, pushed by Republicans wary of Willkie's stances on the New Deal, but that is a more unlikely scenario, and Progressive Republicans upon seeing this shift might move towards Roosevelt in response, key word might.
Then of course Roosevelt could carry the day, but that would be after a series of ballots in which one of the others waves the white flag, most likely Progressive Republicans who see no path to victory for their candidate and wish to go back to business as usual.
Henry Wallace is elected Vice President unless McNary is his opponent, at which point I can see him being narrowly elected since he is favorable to the New Deal and can successfully gain the votes of many Senators wary of Wallace.
