Get a sincere, credible, statement, both in English and in Arabic to their own people from the palestinians's leadership (all factions) and the Arab countries, that if Israel were to yield to Obama's demands (i.e. 1967 boundaries), they would recognize Israel and allow Israel to live in peace as a Jewish state. That should be accompanied by a firm commitment to cease anti-Israel rhetoric/education/propaganda. Even that is a major risk: look at Egypt's discussions about abandoning its 1979 Peace Treaty with Israel.
Hamas says Egyptian mediation has restored calm along Israel, Gaza border (Haaretz)