A poll published on Monday in Israel's Yediot Aharonot newspaper showed Mr Barak trailing 16% behind his right-wing rival Ariel Sharon, leader of the Likud party.
Such a deal has been widely seen as Mr Barak's only hope of reversing the downward trend in his poll ratings before the 6 February prime ministerial election.
A poll published on Monday in Israel's Yediot Aharonot newspaper showed Mr Barak trailing 16% behind his right-wing rival Ariel Sharon, leader of the Likud party.
To make matters worse for Mr Barak, a public sector strike is now entering its second week in Israel, and rubbish has been piling up on the streets.
The BBC Jerusalem correspondent says there is significant support for Shimon Peres to take his place as the Labour Party's prime ministerial candidate - but Mr Barak has vowed that he will not stand down.
Violence has meanwhile continued in the West Bank and Gaza Strip.
An Israeli civilian was shot dead in his car on a road between Jerusalem and the Palestinian city of Ramallah.
The Israeli military said the man, in his 50s, was shot from a passing car. His name was not immediately released.
Earlier, a Palestinian was shot dead by Israeli troops in the Gaza Strip.
Palestinian officials said Mohammad Abu Mussa, 21, was shot in the stomach when Israeli troops confronted stone-throwing Palestinian protesters near Gaza's Neve Dekalim settlement.
Israeli military officials said the Palestinian was aiming a gun at the soldier who shot him.
Palestinian officials said Israeli troops also "abducted" five Palestinians on Monday near the Jewish settlement of Netzarim in the Gaza Strip.
More than 350 people have been killed in the violence which erupted in September - the majority of them Palestinians.
Arafat attack
Mr Barak's decision to call off any further peace talks with the Palestinians until after the election followed a vitriolic speech by the Palestinian leader, Yasser Arafat, at the World Economic Forum in Davos, Switzerland.
Mr Barak's security adviser, Danny Yatom, called Mr Arafat's speech "bellicose, inflammatory and intolerable".
Mr Arafat condemned what he called "barbaric" Israeli aggression against the Palestinians.
He was more conciliatory on Monday, however, after late-night talks with UN Secretary-General Kofi Annan at a Davos hotel.
"We don't want a breakdown in the peace process. We will continue with the peace process despite the difficulties we are facing," Mr Arafat said.
Israel and the Palestinians ended five days of talks at the Egyptian resort of Taba on Saturday saying they were closer than ever to a peace agreement.
Mr Annan said he had spoken to Mr Barak by phone on Sunday and the Israeli leader was encouraged by the outcome of the Taba talks.
Mr Barak's office, for its part, said security contacts aimed at preventing violence between Israeli forces and the Palestinians would continue.
Disputes
Mr Arafat and Mr Barak had reportedly been planning to meet in Stockholm, Sweden, this week to follow up on the Taba talks. But no such summit will now take place.
And, despite the talk of progress in Taba, there was no sign of a breakthrough on the key Palestinian demand of a right of return for about 3.7 million refugees.
Disagreements also remain over control of the Temple Mount, a site in Jerusalem holy to both Muslims and Jews.