Mr Clinton has reportedly proposed that Israel give the Palestinians sovereignty over the al-Aqsa mosque compound, also known as the Temple Mount, while Israel would control the area underneath that includes the Western Wall.
The envoy, Gilead Sher, met Mr Clinton at the White House on Friday to deliver Israel's formal response to the latest American peace proposals.
"We have long odds for that. But we can achieve something to be determined by the president," he replied.
Palestinian officials have given an even less positive view on the short-term hopes for an agreement.
Senior Palestinian minister Nabil Shaath described US compromise proposals on Jerusalem as "nonsense".
'Surface or underground sovereignty'
Speaking on Egyptian radio on Saturday, Mr Shaath complained that the status of Jerusalem in the US plan was not clear.
Mr Clinton has reportedly proposed that Israel give the Palestinians sovereignty over the al-Aqsa mosque compound, also known as the Temple Mount, while Israel would control the area underneath that includes the Western Wall.
Mr Shaath said the Palestinians did not understand the meaning of "surface sovereignty and underground sovereignty."
However, the main obstacle to progress towards a deal is an apparent polarisation of Palestinian and Israeli positions on Washington's proposal that the Palestinians should waive the right of millions of Palestinian refugees to return to homes in what is now Israel.
Mr Barak said on Thursday that his country would never agree to the return of millions of displaced Palestinians.
Reports from Washington suggest that Mr Clinton is preparing to give up the search for a full deal and settle for some kind of declaration that would set a point of departure for future talks under the next US administration.
President Clinton's National Security spokesman P J Crowley said that the president had now heard in detail from both sides and would take a couple of days to evaluate their views before a decision on what should happen next.
Israeli army apology
In a separate development, the Israeli army has expressed regret over the killing of a Palestinian woman on Friday as she hung her laundry in the West Bank town of Hebron.
Arigh Saaber al-Djabali, 19, was shot in the chest on the balcony of her home near a Jewish settlement and died later at a hospital.
"The army expresses its regrets over this incident, but emphasizes that fire from houses against Israeli military positions or against civilians puts residents at peril," an army spokesman said in a statement.
The spokesman said soldiers posted near the Beit Hagai settlement opened machine-gun fire "in response to shots" toward them coming from another house in a Hebron.
Palestinian police and the victims family have contradicted the army's account, saying the Israeli soldiers had not been attacked.