Mr Yasser Arafat returned to Gaza last night from Cairo exuding hope that, while President Clinton has barely two weeks left in office, that period would be sufficient for the attainment of a peace deal.
"That's what we're hoping for, given that President Clinton has promised to make every possible effort before the period ends," he said.
Back in Cairo earlier in the day, the Egyptian Ambassador to Israel, Mr Mohammad Bassiouny, agreed that a deal could be wrapped up in days - provided Israel was ready to comply with the relevant UN resolutions.
And there, of course, lies the problem, as ever. To the Palestinians and much of the Arab world, the UN resolutions require Israel to withdraw from all territory captured in the 1967 war, and to allow all Palestinian refugees and their descendants to return to their former homes inside Israel.
This interpretation is disputed by Israel. But more fundamentally, the notion of absorbing three or more million Palestinian refugees is considered akin to national suicide by almost all Israelis.
In proposing a trade-off - with Israel relinquishing sovereignty at the Temple Mount in Jerusalem, and the Palestinians abandoning the "right of return" for their refugees - Mr Clinton has been trying to forge a viable middle ground. But Mr Barak has said he will not relinquish Temple Mount sovereignty and the Arab League yesterday backed Mr Arafat in declaring the "right of return" to be sacred.
But come what may, Mr Clinton will leave office on January 20th. Mr Barak will almost certainly end a failed, brief term as prime minister on February 6th. And until both sides are prepared to compromise on the matters dearest to their hearts and their history, there will be no permanent peace between them.