President Eisenhower served during the Cold War his entire presidency. He had to make many decisions on how to deal with the Soviet Union. One of his toughest may have been his decision not to directly support the revolutionaries in Hungary 50 years ago.
Wikipedia notes that the Hungarian Revolution of 1956, "was a spontaneous nationwide revolt against the Communist government of Hungary and its Soviet-imposed policies, lasting from October 23 until November 10, 1956. It began as a student demonstration which attracted thousands as it marched through central Budapest to the Parliament building. The revolt spread quickly across Hungary, and the government fell. Thousands organized into militias, battling the State Security Police (AVH) and Soviet troops. The new government formally disbanded the AVH, declared its intention to withdraw from the Warsaw Pact and pledged to re-establish free elections. By the end of October, fighting had almost stopped and a sense of normality began to return. After announcing a willingness to negotiate a withdrawal of Soviet forces, the Politburo changed its mind and moved to quash the revolution. On November 4, a large Soviet force invaded Budapest, killing thousands of civilians. Organized resistance ceased by November 10, and mass arrests began."
Eisenhower clearly sympathized with the Hungarian people. However, any action the United States took beyond offering moral support was dangerous and could possibly have lead to the Third World War. Once the Soviets decided to force Hungary to stay in Soviet bloc, Eisenhower had little choice but to sit back and watch the revolution be squashed.
In the his 1957 State of the Union, he did seek to give refugees some relief. He said, "The recent historic events in Hungary demand that all free nations share to the extent of their capabilities in the responsibility of granting asylum to victims of Communist persecution. I request the Congress promptly to enact legislation to regularize the status in the United States of Hungarian refugees brought here as parolees. I shall shortly recommend to the Congress by special message the changes in our immigration laws that I deem necessary in the light of our world responsibilities. "
The Soviets were not impressed with the help the USA gave Hungary. In fact, they were rather contemptuousus. In a newspaper interview in 1957, Khrushchev commented "support by United States ... is rather in the nature of the support that the rope gives to a hanged man."
Eisenhower's true feeling about the event were made in his final State of the Union Address in 1961. He called the events of 1956 a "brutal Soviet repression of the people of Hungary." He clearly would have liked to have done more (like send in NATO troops to back Hungarian independence from Soviet control) but he wisely made the choice that had no possibility of leading to a nuclear war.