On the issue of Ike's party identification, I remember Cathcon quoting a book called The President's Club along the lines of "Truman was good personal friends with Eisenhower and lobbied him to be the Democratic nominee, to which Ike responded, 'But I'm a Republican.'"
I thought this was very interesting, so I started reading the book while in Barnes and Noble the other weekend, and I will vouch for Ike being a lifelong Republican. One memorable line during the section on when Truman's and Ike's friendship started to fall apart was Eisenhower writing to a friend, "He (Truman) had never even considered the possibility that I didn't share his political view, and let me tell you I didn't; I have been a Republican my whole life."
It should be noted that this has nothing in particular to do with ideology.