Officially the US response to the USSR's threats against Israel (and France and Britain) were "Oh well, bye! Told you not to do this." and THAT is why France and Britain backed down, they knew the US did not have their back. Now, you can go and argue that was just the US bluffing to get the parties involved to back down and leave Egypt, and that may very well be true. But you must acknowledge what truly happened and why. Britain and France BELIEVED the US would not help them if the USSR intervened. And this marks the first time the USSR turned its back on Israel. Despite numerous AH remarks of Stalin being anti-Zionist, he was the first to de jure recognize Israel in 1948 and he had Czechoslovakia in particular give Israel some pretty advanced weaponry (for the Middle East at that particular time). The USSR's anger was less about it being Israel who was involved, and was more directed at the fact that two Western European colonial powers were invading Egypt and the Suez Canal. If it had just been Israel against Egypt you wouldn't have seen a USSR getting involved more than maybe a minor condemnation, and actually might see them accepting a fait accompli in acceptance of Israel having the Suez Canal and a deal to allow Soviet and Eastern European shipping (and military transshipment to the Indian Ocean) in return. In hindsight too many see it as the USSR being anti-Zionist/pro-Arab when in reality it was anti-Western imperialist/pro-third world; it is the results of this that the Arab world turns pro-USSR, not the other way around.