In an ABC News exclusive interview, former British Prime Minister Tony Blair said Clinton has the best type of political mind. "[It] knows where you meet the point of principle and knows where you need the subtlety and the compromise," he said.
Ahead of the talks, Clinton had requested historical background materials concerning past efforts at peace in the region, the ultimately unsuccessful one led by her husband, a source close to the secretary of state said.
"She has this relationship with this fellow who has spent some time talking to leaders -- you know President Clinton -- and she has benefitted from his direct experience," said State Department spokesman P.J. Crowley.
Many regard regard President Jimmy Carter's 1979 Camp David Accords brokered between Israel and Egypt as the gold standard for negotiations, the Clinton source said.
When then-Israeli Prime Minister Menachem Begin refused to authorize the dismantling of any Israeli settlements, Carter's team suggested having the Israeli Parliament make the decision -- and it did. Carter has credited thinking outside of the box and being innovative as the key.
In an interview with James Laue, at the June 7, 1991, National Conference on Peacemaking and Conflict Resolution, former President Jimmy Carter -- who successfully negotiated the 1979 Camp David accords between Israel and Egypt -- preached creativity.
"You have to search for different avenues when you run up against a blank wall," he said. "You have to be innovative...to find some alternative route that might bring you to the same goals."
"You really need to look at life or the negotiation as if it were a chessboard. Anticipating what the next move is and what the next move is after that," said Aaron David Miller, an adviser on the region to six secretaries of state.
Former Secretary of State Henry Kissinger, who negotiated an end to the 1973 Arab-Israeli war, said that audaciousness was part of testing the limits.
"The art of statesmanship is to find a position between stagnation and overextension, hopefully at the outer limit of what is possible," he said during a June 2008 interview on CNN.
In Miller's book, The Much Too Promised Land: America's Elusive Search for Arab-Israeli Peace, he describes how in 1975 the Ford White House, frustrated with Israel during a peace negotiation, claimed it was "reassessing" its Middle East policy.
Years later, Secretary of State Henry Kissinger admitted to Miller the "reassessment" was "theater…there was nothing to reassess." But Kissinger was eager to make the Israelis nervous and eventually they came to the table.
Former President Clinton once suggested that willpower also comes in handy. In his autobiography, "My Life," he described one very late night at Wye River -- where he conducted his own Mideast peace talks -- where his "strategy for success had now boiled down to endurance; I was determined to be the last man standing."
What the negotiators are doing when they're not negotiating might also play a role, Carter has said. By holding peace talks at Camp David, "it was a harmonious environment because Egyptians and Israelis who had been devoting their adult life to killing each other were required to swim in the same swimming pool, watch the same movies, play on the same tennis courts, throw horseshoes together, sit on the same rock and talks. That was all part of it."
ABC News' Kirit Radia, Enjoli Francis and Devin Dwyer contributed to this report.