President Barack Obama's mission of remedial diplomacy to Israel and the Palestinian territories was cast early on as one of modest ambition, a prolonged air-clearing between a U.S. leader and the region's public, disillusioned by his once-ambitious approach to the Middle East.

But over the four-day visit, Obama's broader goal emerged as one both more basic and, perhaps, essential than initially portrayed: to rescue the decades-old idea that Israelis and Palestinians — after years of military occupation, war, terrorist attacks and settlement construction — can live together in side-by-side states between the Jordan River and the Mediterranean Sea.

"The question is whether there can be real peace here," said Tzachi Shickman, a Hebrew University student who attended Obama's speech Thursday at the Jerusalem International Convention Center. "A Palestinian state could bring more attacks on us."