Students of political negotiations might remember the long and difficult discussions in Paris about the shape of the negotiating table for the talks to end the Vietnam War. In the Palestinian-Israeli context, the discussion is not so much on the shape of the table as it is about the participants at the table.
One of the most abused and repeated claims made in Washington is that the Americans cannot want peace more than the parties in the Middle East. The reason why this statement is so false is that the Americans have had a long history of involvement in the Middle East conflict, almost exclusively on behalf of the Israelis. Whether they want to admit it or not, the United States has for decades sided privately with the Israelis while publicly claiming to be neutral. Serious investigation into the motivation for this bias always points to domestic politics as the major, but not exclusive reason for it.