A major stumbling block with the Quartet and one which will ultimately sink all their efforts is their refusal to so much as call Israel the Jewish state.
From news article:
The issue of whether and how to suggest that Israel should be a Jewish state ultimately sank diplomatic efforts by the Mideast Quartet to draft a substantive statement to revive peace talks, sources familiar with the matter said.
The sources, speaking on condition of anonymity, said Israel and the Palestinians - and their effective proxies in the negotiations, the United States and Russia - remain too far apart on that issue and others.
"The heart of the matter was that the only way in which it was going to work as a basis for negotiations was if there was a reference on the one side to '67 lines plus swaps, which was the minimum but not sufficient requirement for the Palestinians, and a Jewish state as one of the goals of the negotiations, which was the minimum requirement of the Israelis," said one source briefed on the negotiations.
The only thing the Quartet is able to do is agree with Hamas for the slow death of Israel.