Since I kicked loose the pebbles that started this, I'll weigh in here.
My own thought was that Rockefeller, the less-than-perfect relations with the right notwithstanding, could pull off the nomination by exercising old-school ticket balancing (similar to what Reagan proposed in '76 IOTL: recall Richard Schweiker as Reagan's would-be running mate then?). My own thought was that Rocky would choose a more conservative Michigan congressman with considerable party leadership experience in the House as his running mate: yes, Gerald Ford.
A Rockefeller/Ford ticket in '68 could, I think, trump pretty much anything the Democrats could put up. Further, I believe that if elected, Rockefeller would bring in Henry Kissinger as first national security adviser, then special envoy to peace talks, sooner than did Nixon IOTL. In fact, I see the Rockefeller administration having a formidable Machiavellian duo formulating foreign policy: Kissinger as national security adviser and Nixon as SecState. Nothing, but nothing even the most devious foreign power might try to pull would get past those guys.