I can't quote the line exactly, but at the '52 convention, the foghorn-voiced senator Everett Dirksen supposedly leveled a finger at Dewey and bellowed something like "you've led us down the path to defeat twice before; you're not going to do it a third time". That suggests that a third Dewey candidacy would be unlikely.
I see Nixon winning and promising Dewey a place in the administration, a reward for supporting him in '52, which I seem to recall he did. I was thinking Attorney General given his organized crime fighting reputation. State would be a longshot, though the idea is sort of based on how Carter named Muskie to State for the last year of his administration. I think somehow getting a supporter of Kissinger in there would be more likely; maybe even Rockefeller.
Nixon getting the '56 nomination seems reasonable, given four years of VP experience on top of Senate and House experience.
Nixon supported Civil Rights so he might do much of what Eisenhower did domestically. I can see him getting close to Rocky and hence Kissinger - scheming to play the USSR and China off each other and drive a wedge between the two seems like Nixon's kind of thing, the way he loved to scheme. There likely wouldn't be a Watergate that early, though, if I understand he was more paranoid about losign after 1960. But, i could be wrong.
Nixon was, in OTL, a consummate foreign policy president with respect to China and the Soviet Union. I could see him doing this, since no other president other than an old-school anticommunist could pull it off. Further, I could see Nixon doing something to either de-fuse or co-opt the Castro-led revolution in Cuba (likely the latter) to ensure that a Soviet satellite wouldn't be set up in the US' back yard. Castro could posture and rant all he wanted, but it would always be with a wink toward Washington, so everyone would know it was all noise/for show and not to be taken seriously. I'd bet in that case it would be pretty much business as usual for Cuban/American relations, although the mob would be on a very short leash, with the worst of their activities curtailed. Could mean an earlier rise of Las Vegas, for what that's worth.
Nixon's VP, ironically, could be Lodge even if he doesn't have a Kennedy ont he other side. Lodge would be a good Eastern establishment kind fo guy who would be experienced in foreign policy. Rockefeller mighht seema bit young and inexperienced - Nixon might want someone older. he's only be 43 duringt he electionc ampaign.
Not entirely sure about this. Yes, Lodge's establishment credentials were impeccable but so were those of a lot of other eastern Republicans at the time. I'd suggest instead Theodore McKeldin, the governor of Maryland (see
http://en.wikipedia.org/wiki/Theodore_McKeldin). He had fine establishment credentials in his own right, as well as being governor of what could be a swing state with solid urban credentials.
Dulles would still be SecState; guessing Dewey would be Attorney General with perhaps an eye on State given Dulles' less-than-perfect health. Rocky might be ambassador to the UN, or perhaps SecInterior as an entry-level cabinet post and an eye on moving up.