The U.S. mediator for the Middle East, Dennis Ross, shuttled between Israeli and Palestinian politicians for the third day on Thursday in search of a new formula to bridge the steadily widening gap between them and enable negotiations to resume.

Ross gave no indication of his progress. But in the highly charged political air since the resignation of Israeli Foreign Minister David Levy at the start of the week, newspapers were filled with speculation and anonymous reports.

The central question among Israelis, and probably for Ross, is whether Israeli Prime Minister Benjamin Netanyahu’s government is capable of surviving any decision. Levy’s defection has left Netanyahu with a scant 61-59 edge in Parliament, and ministers on both sides of the debate have vowed to bring the government down if it either cedes land, or fails to.

On the left, Defense Minister Yitzhak Mordechai, a moderate in the Cabinet, declared in an interview that he would resign if Israel made no withdrawal in the next three months.

On the right, Rehavam Zeevi, the chairman of the ultra-nationalist Moledet Party, told the prime minister: “Let me tell you where we stand: We will vote no-confidence the moment the Cabinet decides on the substance of the redeployment, on percentages or on a timetable.”

Ross’ problem is that the United States has repeatedly bowed before the argument that Netanyahu is hamstrung by his unstable government. This time, U.S. officials said Washington would insist that Israel live up to its obligations to make further withdrawals, or redeployments, in the West Bank.

At the core of the current debate is Israel’s obligation to make three additional withdrawals even before a final settlement is reached. Netanyahu pledged to do so a year ago, but his proposal for a marginal first withdrawal was rejected by the Palestinians.

The Americans now insist that Netanyahu make a “credible” second redeployment, which means more than 10 percent of the West Bank. The prime minister has reportedly told the Americans that he will do this if the Palestinians agree to forgo a third redeployment and enter immediately on final-settlement talks. The Palestinians reject this notion out of hand.

According to officials who have met with Ross, the mediator has tried to shape a new package that would impose strict security conditions on the Palestinians in exchange for credible withdrawals. But an initial agreement mediated by the United States, and accepted by both Israeli and Palestinian security chiefs, was thrown out by Netanyahu, reportedly because it drew a parallel between Palestinian and Jewish militants.