And he saw how today's Republican Party functions and what it stands for, what would he be most surprised about?
Hell, you could put in Nixon for this question too.
He was a major power projectionist, and he was deeply interested in foreign policy. In fact, I think his first inaugural address was devoted entirely to foreign policy, so I think what would surprise him most are two things: most favored nation trading status of China (although that was accomplished by a Democrat president) and our invasion of Iraq (incited by a Republican administration.) Domestically, I think he be most surprised by the sad state of the physical infrastructure in the United States (accomplished by both parties.)
As for the evolution of the Republican party, I'm not sure what he'd think. I think he'd be dismayed, but not surprised by its intransigence and brinksmanship. He often had to deal with the Old Guard in his day, so the arrogance in the GOP leadership now probably wouldn't be a huge surprise. Just a disappointment. He might be a bit taken aback at the polarization in both parties beginning in about the 1970s. I'm not sure anyone from the 50s and 60s expected that.
Then again these things are cyclic, so it depends upon how well Eisenhower reads history. The Republican party was its most conservative just after the turn of the 20th Century. Then Roosevelt was elected and throughout the first two-thirds of the 20th century a slow progressive drift ensued. Eisenhower's presidency was near the end of this period. He might have assumed that it would continue. Then, starting in the early 70s, a rightward drift occurred, especially during the 1980s. This was partly due to the realignment of the southern voters during that period, so that conservatives were replacing more moderate Republicans outside the southern states and conservatives were replacing moderate and conservative Democrats in the South. (This also had the effect of making Democrats more progressive over that 40-year period, although with democrats the trend is not as marked. Some academic studies show republican correlations of about 0.95 but only about 0.84 for Democrats. Still, the trend is there.) Of course this is all fairly well documented, but the question is how would it strike Eisenhower. My standing assumption is that if you could wake the dead, just about any former US statesman would be vaguely disappointed at the whole US political culture, but most of them were pretty smart guys, so I doubt that they would be terribly surprised.
