In 1960, David Pietrusza wrote that immediately after the 1960 Democratic Convention, many oil barons were threatening to bolt the Democrats for Nixon. Rayburn was apparently so furious that he threatened them with an axe of the depletion allowance if JFK/LBJ lost Texas, not just the election. So let's say Nixon performs well in the first debate and Ike does a bit more campaigning, Nixon ekes out a win, including Texas.
Does Rayburn follow through post-election, and if so what are the consequences? I can see it as a catalyst for an informal split similar to the scenario posited in AATW.