Ike warned against getting involved in a land war in Asia. I suspect a land war in the Mideast would also not be his cup of tea. As I recall, there was no US invasion at the time of the Suez crisis.
The interesting thing is that there are still 2 sizable strands of Republicanism which oppose Bush's "excellent adventure" in Iraq. Moderates would like some justification for Americans killing and being killed overseas. And the Pat Buchanan branch, which is against "nation-building"-- (as Bush himself stridently was during the 2000 campaign)-- and against foreign entanglements generally.
Bush's so-called foreign policy is more a perversion of Wilsonianism than anything Republican.
LH is also, it appears, right about the 1960 election. But another factor, I've read, is that Kennedy exploited the anti-Communism mania by loudly proclaiming a "missile gap" which he knew actually did not exist, since he had been briefed about the defense posture of the US.