Rockefeller would do better than Goldwater in traditional Republican areas, winning Vermont, Maine, New Hampshire, and maybe some of the plains states. Rockefeller might do worse overall electorally than Goldwater if he doesn't win his home state of New York, but in the popular vote he'd do better, losing many states by much smaller margins. The Republicans take smaller losses in Congress than OTL, though they don't win the scattering of seats they won in the Deep South.
A segregationist third party, led by Thurmond or Wallace probably, arises and sweeps the states that OTL went for Goldwater in the South. Strom Thurmond would stay a Democrat in 1964 or become an independent; maybe he'd switch to the GOP if they nominated Goldwater or another conservative in 1968.