Talks were under way to try to persuade the ultra-Orthodox Shas, which has 17 seats in the Knesset, to remain rather than undermine the government at a potentially crucial point in the peace process by shrinking Mr Barak's support in the 120-seat Knesset to 51 MPs.
Shas said it was angered by the government's failure to fund the party's hopelessly bankrupt education and welfare system. Yesterday it agreed to a request from Mr Barak to suspend its walk-out for 24 hours, which suggested a deal will be brokered.
If Shas sticks by its decision, the government is unlikely to fall, as it can muster support from among parties outside the coalition - the six- member secular Shinui party has already offered to step into Shas' shoes. But it weakens Mr Barak's hand and complicates the peace talks when there appears to be progress on several fronts, albeit fragile.
Perhaps the biggest worry for Mr Barak is the impact of a Shas defection on the Syrian talks. Any accord involving the return of the Golan Heights, which Syria demands as a prerequisite to a deal, will go before the Knesset. If approved, it will be put to a referendum, in what some expect to be the most bitter internal battle in Israel's political history.
Shas has held back from committing itself to a position, in the hope of squeezing more concessions from the government. But if it leaves the coalition and comes out against a Golan withdrawal, Mr Barak will struggle to secure the referendum majority his government must achieve to survive. Nearly 431,000 people voted for Shas in this year's election, making it the third-largest party in the Knesset.
Efraim Inbar, a specialist in Israeli politics at Bar-Ilan University, said: "There is a good chance of it being resolved, but if this goes on we might very well see the beginning of the end for the Barak government. He cannot go on with the peace process if he doesn't have a large consensus behind him."