LBJ received 6,096,989 to Barry Goldwater's 5,993,384 in the 11 Confederate states (Obviously not including the 210,732 votes in Alabama that went to the unpledged Democratic slate). Considering that the vast majority of the voting populations in Southern states in 1964 were white, the answer is most likely (narrowly) Lyndon Johnson.
Of course we could throw the non confederate Southern states like WV, OK and KY in which case Johnson would be safely winning the Southern White vote.
If Johnson carried the South by no more than 1%, Goldwater carried the Southern white vote. There were
some AAs voting, especially in outer Southern states such as Tennessee, and they obviously backed LBJ with >90%.
