In September, the United Nations General Assembly will consider a proposal to recognize Palestinian statehood. Ashrawi said that will lead to membership and its benefits within the international community.

"It means you get access - you have access to all the judicial accountability you need within the U.N. [United Nations] system," she said. "And then, you have the recognition that you do have boundaries."

Peled predicts the U.S. and other countries won't allow it. "To go through the United Nations for recognition, is not the correct path. I think that is the strongest message that is coming out of this last week's visit."

That, Ashrawi said, would be a mistake. "If you block us from the U.N., from getting accountability from Israel, from trying to get protection for Palestinians, by peaceful means, by non-violent means, then it seems to me you leave us with the option of violence, as the only thing that works."

If so, the Arab Spring holds little promise of thaw between Israelis and Palestinians.