Without reading the dozens of paragraphs above, I need to chime in to remind everyone that "Rockefeller Republicans" had some of the most brutal views on crime, urbanism, and race in the history of the country. The movement is literally named after the governor best remembered for his response to the Attica prison riots. They were not suburban intellectuals; they were the last political movement appealing to the concerns of a now politically extinct class: upper-class urban whites. Their "moderate" views on abortion and gun control largely stem from paranoia regarding black crime, and the common view of them as broadly "liberal" is misguided, as is liberal nostalgia for them.
P.S. Having written this out, I did go back and see that Al and NCY largely hit the mark.
I'll tack on that the narrow WASPishness (at least in public reputation) of the Rockefeller set prevented them from appealing to ethnic minorities, which would have preserved their power another decade or so. And the acceleration of Northern white fears after 1964 pushed voters past what even the Republicans were offering. Instead, ethnic voters went for Wallace (before later abandoning the cities) while wealthier voters abandoned the cities as soon as possible for Rye, Greenwich, Orange County, etc., forming the basis for the Reaganism of the 1980s.
And none of this is to say that there weren't "liberal Republicans" as there are today. But they were never a coherent enough movement appealing to enough voters to, say, elect a President. Or even a Governor of New York.
The "Tough On Crime" aspect of Rockefeller was not a consistent part of his record. He was the Governor who signed the bill abolishing the Death Penalty in NY.
Rockefeller pushed through a Draconian bill to give life sentences to Drug Dealers as part of his drive for a 4th term in 1970, but he did not enact the full gamut of "tough on crime" legislation. He used force to quell the riots at Attica, but force was justified; that situation was way too out of hand. That being said, he began to implement the reforms called for in the wake of the riot at Attica.
That being said, Rockefeller did have a "conservative" side to him. I remember discussing Rockefeller with one of my teachers (a Ramsey Clark liberal) who agreed with me when I asked him why conservatives hated Rockefeller so much when he seemed, aside from being a big spender, to have much in common with them. Rockefeller DID move to the right after his 1968 run for President; he was more conservative in 1970, he nominated Nixon in 1972, and he was conservative enough to be selected as Ford's VP. Most people did not view him as a "Liberal Republican" when he died; they just viewed him as "not a conservative". The term "Moderate Republican" doesn't really fit, however. He was for big government and big spending in a way that Eisenhower cringed at.