Both, left and right have proved that just peace treaties pay out (see Jordan and Egypt). Both, left and right have failed to settle the conflict with Lebanon, Syria and the Palestinians. In particular, the Lebanon withdrawl that resulted in a 6 year period of calm had not been followed up by diplomatic moves towards a peace treaty - neither by the left nor by the right.
Israeli PM to Palestinian President Abbas: We must fight terror together (Haaretz)
from the article: They fell asleep at the wheel