Here's a too-short explanation of the situation from my travelogue on The Monk's visit to Budapest in 2003:
Hungary was on the wrong side of both world wars -- in WWI it was part of the Austro-Hungarian Empire (although it was the junior partner) and lost more than just Austria when the Empire was split at Versailles. Instead, large parts of what were ethnically Magyar, and nationally Hungary, became territory of other countries -- Western and some Southern areas of Hungary were included in Yugoslavia, some northwest and northern lands became part of Czechoslovakia, and Transylvania and much of eastern Hungary was seized by Romania . . . In World War II, Hungary sought to appease the crocodile only to be its last meal -- its dictator's compliance with Hitler did not prevent Hungary from being conquered, nor did it prevent Hungary from having the second-highest number of Jews killed in the Holocaust despite the fact that deportation of Hungarian Jews didn't even start until 1944. Ultimately, Hungary was on the wrong side of the WWII peace -- included in the Soviet "sphere of influence" under Yalta and soon after a client state of the USSR.
In 1956, Hungarian premier Imre Nagy (imm-ray nah-dee) sought to relax Communist controls and grant freedoms (including, ultimately, elections) to the Hungarians. The USSR deposed him and set up a puppet government; students led riots and the Soviets sent in the soldiers. The students led attacks against the USSR soldiers (and created the "Molotov cocktail" for Evgeny Molotov -- the Soviet official in charge of pacifying Hungary) and the rest of the world stood by and watched (Eisenhower reportedly regreted this later). The Soviets quelled the riots, squashed dissent and dissenters, set up show trials for Nagy and some followers and gave Nagy to the horrific Gheorghie-Dej regime in neighboring Romania, which later executed him. Simply stated, neither the Soviets nor Romanians are well-liked in present-day Hungary
The response to the Hungarian Uprising was one of the two low points of the Eisenhower Administration. In answer to a question on whether he had made any mistakes during his presidency, Ike reportedly said "two of them, and they're both on the Supreme Court" in reference to Earl Warren and William Brennan. But Ike's failure to make a strong statement condemning the USSR's actions in Hungary, and his fit-of-pique reaction to the Suez operation launched by the French, British and Israelis that same year, stand as two of the worst misjudgments of the Cold War.
This is more of a day to celebrate the bravery of the Hungarians than bash the cluelessness of Eisenhower. In that vein, David Pryce-Jones offers a fine summation of the result:
More than epic, it was Homeric, something to remind mankind of the heights we can rise to in order to be free. Dragged along by events, the newly installed Prime Minister Imre Nagy did his best, but he had behind him a lifelong career as a Communist, and he made the fatal mistake of trusting the Russians. We know now that Khrushchev and the Politburo in the Kremlin always preferred a military solution to a political compromise with Hungary. They tricked the Hungarians into coming to arrange a treaty, arrested the delegation, sent the tanks in, smashed up everything, judicially murdered Nagy and at least 300 others, imprisoned over 20,000 and drove 200,000 into exile in the West.
“Help Hungary. Help!” was the final appeal on the radio, put out by Gyula Hay, the playwright and in his day a veteran Communist too. In sad fact, the United States did nothing, making it plain that the Soviets could do their worst. On hearing that a revolution had broken out, President Eisenhower limited himself to saying, “The heart of America goes out to the people of Hungary.” Heart is all very well, but what about muscle? Robert Murphy, then undersecretary of state and an experienced trouble-shooter, summed up Washington’s failure: “Perhaps history will demonstrate that the free world could have intervened to give Hungarians the liberty they sought, but none of us in the State Department had the skill or the imagination to devise a way.”
Too bad for Murphy and the US, some things really do not change.