Eisenhower did not intervene in the Soviet put down of the 1956 Hungarian Revolution. He recognized that the risk was not worth it.
The U.S. vice-president R.M. Nixon said that: “We couldn’t, on one hand, complain about the Soviets intervening in Hungary, and, on the other hand, approve of the British and the French picking that particular time to intervene against [Gamel Abdel] Nasser.” Despite earlier demands for the rollback of Communism and of the Leftist liberation of eastern Europe, Dulles told the USSR that: “We do not see these states [Hungary and Poland] as potential military allies.”
In 1998, the Hungarian ambassador Géza Jeszenszky criticised Western inaction in 1956 as disingenuous, recalling that the political influence of the United Nations readily applied to resolving the Korean War (1950–1953). Moreover, the study Hungary, 1956: Reviving the Debate over U.S. (In)action During the Revolution confirms that the Eisenhower government did not intervene to the Hungarian Revolution – which occurred in the Soviet sphere of influence – because the USSR would have responded with a nuclear war.
I find THAT a "most convincing, rational case against intervention"...
;>)