Obama has now supported Israel's right to self-defense and has been discussing a ceasefire with Turkey and Arab states. It is now the job of the United States, whose president has spoken and acted as if the government in Egypt is his client, and all the vaunted leverage that the U.S. government says it has gained in the Arabic-speaking world through various actions over the last four years. America and Europe need to use the aid and backing they have given to Egypt as a way to get something in return. And if, despite Egyptian efforts, Hamas still refuses a ceasefire then the U.S. government and other Western states might well rethink their negative attitude toward an Israeli ground offensive.
So far, Hamas has been turning down the efforts by Egypt and Qatar to broker a ceasefire, making huge and ridiculous demands. Hamas is banking on the idea that the suffering of Gaza's people--a suffering that it adds to and fictionalizes--will bring enough Western sympathy to force Israel to stop fighting without conditions. It is not in anyone else's interests to let this happen.