I'm going to assume that George Wallace doesn't launch an independent candidacy.
Goldwater narrowly wins, 288-250. I'm assuming LBJ ultimately endorses McCarthy, but doesn't lift a finger for him in Texas (or anywhere, for that matter). This election would be radically different from the "real" one, of course... as you can see, the results would be much closer to present-day alignments than Nixon vs. Humphrey vs. Wallace.
For one, there would be no ambiguity on civil rights for the GOP. Nixon managed to steer a "middle course" between the Democrat and the Dixiecrat; Goldwater would be strongly identified with segregation, just as he was in 1964. McCarthy would clearly attack LBJ and the Vietnam War; Goldwater would be out in right field again, somewhere between Nixon's and Wallace's real-life positions.
Bottom line: Goldwater wins at least 75 percent of the southern white vote. He would be approaching >95% in several states, particularly in Mississippi and Alabama; in a few isolated counties bossed by neo-Confederates (e.g. Plaquemines in Louisiana), I wouldn't be surprised if, literally, every white vote was for Goldwater. On the other hand, Humphrey would probably win around 95 percent of the black vote, which would help him more in the Northeast and Midwest than in the South.
and McCarthy wins a lot of dovish, "progressive" or "liberal" Republicans in the northern tier, from New England to the Pacific Northwest. I'd guess faithful Vermont, at least, would return to the GOP and vote Goldwater this time.