Now it's his turn. After the elder George Bush, Bill Clinton and George Bush the younger, Barack Obama has became the fourth consecutive American president to seek international diplomacy's hitherto impossible prize: Israeli-Palestinian peace.
The roll-call of place names associated with such efforts since the end of the first Gulf War in 1991 is long: Madrid, Oslo, Wye, Sharm el-Sheikh, Camp David, Taba and most recently Annapolis. One thing, though, they have in common: failure. And so to Washington, September 2010.
Just 24 hours after formally winding up the US combat mission in Iraq, Mr Obama yesterday began two days of intensive summitry with separate White House meetings: first with Israel's Benjamin Netanyahu, then with the Palestinian President, Mahmoud Abbas.
A dinner last night followed, with the region's most important supporting players, King Abdullah of Jordan and Egypt's Hosni Mubarak, among the guests, before Messrs Abbas and Netanyahu get down to business in earnest this morning in face-to-face negotiations at the State Department. The ceremony will be presided over by Hillary Clinton – who will earn her place as one of the greatest secretaries of state in history if she can succeed where such redoubtable predecessors as Henry Kissinger and James Baker could not.
"This time it's different," insist an admittedly dwindling band of optimists, echoing the refrain of losing sports teams and gung-ho stock market speculators throughout the ages. But is it different?
Mr Obama's goal is the same two-state solution sought by presidents Clinton and Bush before him, based on agreement on the four core issues of security, borders, Palestinian refugees displaced by the creation of Israel and the status of Jerusalem. Like George W Bush, he has set a one-year target for a deal.
The contours of any viable final settlement have long been known: secure borders perhaps monitored by outside forces, the return of the vast bulk of the West Bank to the Palestinians, along with territorial compensations elsewhere for areas where the density of Israeli settlements makes retrocession impossible. There would be a purely symbolic right of return for refugees to Israel proper, while both states would share Jerusalem as their capital.
In other words, the diplomats can come up with a solution. What has always been lacking is the political will to accept it. "We don't need to re-invent the wheel," Saeb Erekat, the chief Palestinian negotiator, said yesterday. "The time is not for negotiations, but for decisions."
If those words are evidence of Palestinian frustration at what they see as Israeli procrastination – especially on the issue of settlements – Mr Netanyahu ostensibly shares those feelings. After months of indirect or "proximity" talks brokered by George Mitchell, the US Middle East envoy, the Israeli Prime Minister is now ready for fortnightly summits to achieve a deal.
As usual, everything is at the mercy of extremists, on both sides. Late on Tuesday, the military wing of Hamas, the Islamist Palestinian group and bitter rival of Mr Abbas's Fatah movement, claimed responsibility for killing four Israeli settlers travelling near Hebron on the West Bank.
After a long lull in such incidents, the shootings were plainly designed to undermine the authority of Mr Abbas and derail the new talks even before they began, by demonstrating that the Palestinian leader cannot provide the security that Mr Netanyahu insists is an essential precondition for serious Israeli concessions.
A furious Mr Abbas swiftly condemned the attack, as did Mrs Clinton and the Israeli Prime Minister. Yesterday, the President himself made an unscheduled appearance in the White House Rose Garden with Mr Netanyahu, to express his disgust at the "heinous and senseless" slaughter, and the "unwavering" commitment of the US to Israel's security. The stakes are that high.
Even so, within hours of the shootings, some settler groups vowed to break a government-imposed halt to new Israeli building on the West Bank. If so, they would merely be bringing forward the first – and perhaps fatal – challenge for the negotiations: the fate of the 10-month partial settlement freeze imposed by the Netanyahu government that expires on 26 September.
The Prime Minister, confronted by the threat of a right-wing rebellion that could bring him down, may well be unable to extend the freeze. But if he does not, and the settlement expansionists prevail, then Mr Abbas has already declared that he will pull out of the talks.
In his separate bilateral meetings yesterday, Mr Obama undoubtedly sounded out his guests on a compromise formulation that would satisfy both sides. But there is no guarantee that compromise is possible – and that hard political realities will not once again trump the diplomats' best efforts. And the settlement issue lies in the foothills of the journey to the summit. In short, it takes a reckless disregard of history to believe that this time it really is different. But optimists there are.
They rest their case on the reduced level of violence. They point to a better functioning Palestinian state on the West Bank, and to the sharp fall in settlement building, especially since the uproar in March when Israel announced the construction of 1,600 new housing units in contested East Jerusalem at the very moment Vice President Joe Biden was on an official visit. They claim large, conflict-weary majorities of both Israelis and Palestinians support a two-state solution.
Then there is the "Nixon-goes-to-China" argument. If any Israeli government is to cut a deal with the Palestinians, it must be a government led by a hardliner such as Mr Netanyahu. Finally, there is the biggest novelty of all in an otherwise familiar equation – Mr Obama himself.
No president in modern times has spoken so movingly about the plight of the Palestinians, none has placed such emphasis on improving America's relations with the Muslim world and none has been as prepared to take on Israel – up to a point at least. This week, moreover, he delivered, by ending the combat mission in Iraq, the intended prelude to the complete departure of all US troops by the end of 2011.
But Mr Obama's determination is a two-edged sword. Yes, he is acting much earlier in his presidency than his two predecessors but that carries added risks of its own. Already, this president has clashed more publicly with an Israeli prime minister than any of his predecessors. But Mr Obama faces what could be a tricky re-election bid in 2012, in which he will not want to have added the powerful American Israel lobby to the list of his opponents.
What's top of the agenda?
Keeping the talks going at all. The immediate challenge for Obama is to find a formula which can reconcile Netanyahu's reluctance to prolong a partial freeze on settlement building beyond 26 September – probably strengthened by Wednesday night's killings – and Abbas's threat to pull out of talks if he refuses.
If the talks do survive, what will they be about?
What they've always been about: ending the Israeli occupation which began with victory in the 1967 Six Day War when it took control of the West Bank and Gaza. And that means agreements on borders, which the Palestinians believe must be based on the pre-1967 lines, the future of Jerusalem, which the Palestinians want as a shared capital, and the fate of the families of refugees that were forced from or fled their homes in what is now Israel during the 1948 war.
So can this gap be bridged?
The question is whether the maximum Israel is prepared to move is enough to match the minimum any Palestinian leadership could accept. Most informal plans assume that Israel would get a variation of the pre-1967 lines to bring the big settlement blocs into Israel in return for a land swap that would give the Palestinians 22 per cent of historic Palestine. Jerusalem would be re-divided into the Jewish West and the Arab East. There could also be major compensation for refugees, and for those in camps in Lebanon, Syria, and Jordan to return to the West Bank if they chose, with – perhaps – a token return of a few thousand to Israel.
So what's the problem?
This Israeli government, even more than its predecessor at Camp David, has big ideological issues, for example with dividing Jerusalem or recognising even a notional "right of return" for the 1968 refugees. Anything else?
Netanyahu wants to start the talks by discussing security, principally along the Jordan valley – the border of the putative Palestinian state. This could be solved with an international force supervising an Israeli presence. But this may not be enough for Netanyahu.
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