Rockefeller himself ran for the 1968 nomination. The conventional wisdom of the punditry at the time was that the Republicans should nominate Rockefeller because tricky Dick was to conservative to win.
Of course, we now know that the country and the Republican Party were changing. The nomination of Barry Goldwater was not a disaster, but a sign of changing times in the party. The Gipper himself entered the 1968 primaries. The conservative movement left Nixon behind or perhaps more accurate, he didn't keep up.
Nixon had Pat Buchanan by his side beginning in 1966 and as the story goes Nixon would ask Buchanan “What do they want?” when it came to conservatives.