During the 1956 Suez War, the United States used economic blackmail to force Britain, France and Israel into withdrawing. The British and French eventually agreed to a ceasefire, but Israel wanted to keep the Gaza Strip hold the Sinai until it extracted some concessions and promises from the Egyptians.
Eisenhower threatened to cut off aid to Israel, which at the time consisted only of food and economic assistance, to freeze donations by American Jews, ban the purchase of Israeli bonds, and even threatened UN sanctions and expulsion from the UN. Israel was persuaded to withdraw after the USA agreed to guarantee free navigation for Israeli ships.
What would have happened if Ben-Gurion refused to cave? Keep in mind that the Israeli-French relationship was beginning to bloom at this point. Israel could have gotten the French to veto sanctions in the Security Council. The General Assembly might impose sanctions, but they would not be mandatory, simply a reccommendation (the "uniting for peace resolution was not binding under international law: it simply gave legitimacy to Coalition actions in Korea carried out without Security Council sanction). UNGA has called for sanctions on Israel before to absolutely no effect.
However, what would have happened had the US imposed its own sanctions? And how would the Soviet Union have reacted to Israel's refusal to withdraw?