You won't find many who don't want to see peace in the Middle East, but the good-on-paper solutions face many real hurdles.
A demand that would never be accepted by the Palestinians: Israeli Prime Minister Benjamin Netanyahu supports a two-state solution that would shore up the territories for the long run through economic rebuilding efforts. But he also wants a Palestinian state to recognize Israel as a Jewish state. This would run afoul of most Muslim believers in the region, and any Palestinian leader who might accept this demand would likely meet the fate of Anwar Sadat.
Another demand that would never be accepted by many Palestinians: The cessation of attacks upon Israel. The militant wings of Hamas and Fatah -- the Izz al-Din al-Qassam Brigades and the Al-Aqsa Martyrs Brigade, respectively, as well as numerous militant shoot-offs -- are too invested in the destruction of Israel, and the militant wings are inextricably linked to their respective parties.
The question of Jerusalem: A sacred city to Judaism, Christianity and Islam, the split of Jerusalem is a deal-breaker to many and unavoidable to others. The Arab Peace Initiative, also known as the Saudi peace plan, would hack off the old part of Jerusalem for a Palestinian state. This plan is backed by neither Israel nor the West; along with religious and territorial considerations, the question of security is brought up in such a split.
The constituencies: Though politicians may be ready to make a deal, both Israeli and Palestinian leaders are keenly aware of the fear or anger that could result among their people by brokering a solution. The pullout from the Gaza Strip as a good-faith gesture and subsequent violence, for example, put more hawkish leadership back in charge in Israel.

