That ghost was the Camp David talks of summer 2000, when US President Bill Clinton publicly held Yasser Arafat, the then-Palestinian leader, responsible for the breakdown of the negotiations, despite an earlier promise to blame neither side if they failed.
Mr Clinton's finger-pointing breathed life into the accusation from Ehud Barak, Israel's prime minister, that there was "no Palestinian partner for peace"; brought about the collapse of the Israeli peace movement, and ultimately sanctioned the decision of Mr Barak's successor, Ariel Sharon, to invade the Palestinian-controlled areas of the West Bank.
A decade later, the Arab League ministers did not want to expose Mahmoud Abbas, the Palestinian president, to a similar charge from Barack Obama.
The decision's dual purpose was to throw the spotlight squarely back on Israel as the recalcitrant party, and allow the White House to continue to pretend the talks are still on track.
The League's new deadline was chosen precisely to appease Washington. Mr Obama's most pressing concern is shoring up his Democratic Party's vote at the congressional midterm elections in early November. Neither Israel nor the Palestinians wants to be seen walking away from the president's peace initiative before then.
"The Israeli government was given the choice between peace and settlements, and it has chosen settlements," the chief Palestinian negotiator, Saeb Erekat, said last Friday.
Benjamin Netanyahu, the Israeli prime minister, spun events the other way, arguing implausibly that the Palestinians should have engaged more decisively in talks during the 10-month partial freeze on settlement growth, which expired two weeks ago. "The questions need to be directed to the Palestinians: why are you abandoning the talks?" Mr Netanyhau said last Thursday.
Rather than investing wasted energy in doomed talks, the two sides appear to be adopting the same alternative strategy: cutting a deal directly with Washington that circumvents the other party.
At the weekend it was reported that Mr Abbas had told Arab leaders he was considering asking the US president to recognise a unilaterally declared Palestinian state in the whole of the West Bank.
Mr Erekat told Reuters another option might be a request for a United Nations Security Council resolution calling on member states to "recognise the state of Palestine on the 1967 borders".
Mr Netanyahu, meanwhile, is reported to be working on a counter-offensive he hopes will win Washington's approval. Michael Oren, the Israeli ambassador to the United States, officially confirmed to The Washington Post last week that the Obama administration had offered Israel a range of generous diplomatic, security and financial "incentives" to secure a few months' extension of the partial moratorium on settlement building.
Mr Netanyahu is reported to have turned down the offer but only, it appears, because he believes he can win a more valuable concession. His real aim, the Israeli media reported last week, is to persuade the White House to reaffirm a promise made in a 2004 letter from Mr Obama's predecessor, George W Bush, that Israel will not be required to withdraw to the pre-1967 borders in a peace deal.