Support of Israel Against Existential Threat Resolution of 2013 - Expresses the sense of Congress that: (1) the United States should ensure that Israel is able to adequately address an existential Iranian nuclear threat, (2) the Secretary of Defense (DOD) should seek related opportunities for defense cooperation and partnership on military capabilities where appropriate, and (3) the delivery of the S-300 air defense system to Syria would pose a grave risk to Israel and the United States supports Israel's right to respond to such threat.