The Rockefeller wing would not concede to a Conservative. In 1964, they put up a fight. Some people claim that Goldwater was an accepted sacrificial lamb for an election the Republicans knew they would lose, but that was not the case. Rockefeller screwed himself over with his divorce and remarriage, and Goldwater was rammed through on a wave of populist support the establishment never expected and did not know what to do with. And though Rockefeller remained in the race, his support had evaporated with Liberals and Liberal organizations. It was a bit like Romney 2012: the party kept trying to prop up a candidate to stop Goldwater, and it all crumbled. Scranton couldn't and entered probably too late. Romney did not run. Etc.
So that shows what you'd have in 1968. In this scenario, there would not even be a Goldwater 1964 and I believe Nixon would have a Pax Republicana for the decade. On the whole, that may be a good thing. The Liberals and the Conservatives hated each other. The Liberals saw the Conservatives as a bunch of radicals (and it doesn't help that angry masses of people like that reminded many of Nazis; the War was only 20 odd years prior). They thought they poisoned dialogue and were dangerous. The Conservatives saw the Liberals as "Me Too" Republicans, who went along with what the Democrats said and did. And they saw them as fake Republicans and elitists. But they voted even for Rockefeller Republicans because they felt that in their own time of need, the Rockefeller Republicans would do the same. 1964 showed that was not the case.
Much as between the Northern and Southern Democrats, there was a delicate balance within the Republican party. 1964 exploded that. Without 1964, things are going to be better. And Nixon is the perfect man to bridge the gap over the course of the 1960s. However, 1968 may be tougher. That said, who will the Conservatives rally around? Goldwater may not run; he did not want to in the OTL and was only pressured to by movement Conservatives. Reagan may not even be a successful politician. He would not have campaigned for Goldwater in 1964, and with a Nixon White House, I doubt you would have the 1966 Republican successes of the OTL. 1968 may sew some seeds of dissent, but it may be a situation where the Conservatives are angry that Rockefeller is the likely nominee but have no one to put up against him. Or there is a moderate nominee to bridge the gap, but the Conservatives wish they had a Conservative candidate.
It seems at some point, things have to realign regardless. Each of the parties are really two elements, where the national parties make efforts to keep things balanced and equal to avoid civil war.