This in turn suggests a Stassen Cabinet including John Foster Dulles as Secretary of State (conventional wisdom has it that he would have been Dewey's choice, and we know he was Ike's choice four years later), and quite likely Dewey himself as Attorney General. I have doubts, though, that Stassen would have been able to convince Ike to resign his commission to become Secretary of Defense--unless there was a sub rosa promise made that he'd get to rein in MacArthur once and for all.
In any event, a Stassen nomination in '48 and his subsequent election quite likely obviates an Eisenhower presidency. I'm not familiar enough with Harold Stassen apart from some reading to gauge how he would have fared against McCarthy--or even if McCarthy would have gained any traction at all with Stassen in the White House as opposed to Truman. With a no-nonsense anti-communist like Dulles running the State Department, I'm wondering if McCarthy wouldn't have had much of a basis for his re-election bid in 1950, and might have lost in the mid-terms.
Possibly Korea would have been prosecuted somewhat more vigorously / capably (?) if, say, Ike were in charge as opposed to MacArthur, leading to terms more favorable to what we know of today as South Korea. In turn that might mean that the Pyongyang regime would be on shakier ground from the outset--and perhaps might have fallen during the late 1980s/early 1990s.
I'd bet Stassen's successor would have been Adlai Stevenson: the time was more or less right, and it's difficult to imagine that Stassen's VP (can't argue with Warren, by the way) would be elected. John Gunther said that Warren would make "…a tolerable President of the United States…", which isn't exactly a ringing endorsement when it was written in 1947. Possibly the '56 GOP nominee might have been William Knowland, with NJ governor Alfred Driscoll as a running mate: that might have yielded a rather high-level campaign, with the Dems running Stevenson and either Kefauver or Kennedy.
Long story short: the '50s and beyond might well be decidedly different than we knew them to be.