If the 2005 state budget does not pass by 31 March, Sharon must step down and new elections will be called, endangering his plan to withdraw from the Gaza Strip and four West Bank settlements this summer.
Thirteen of 40 Likud legislators oppose the pullout plan and have said they would vote against the budget, depriving Sharon of a majority in parliament. It remains unclear whether all rebels will vote no, since they could lose their parliamentary seats after new elections.
Addressing female members of the Likud on Thursday evening to mark International Women's Day, Sharon said his government could easily fall over the budget.
"We face a problem today. The problem is that there is a group within the Likud that threatens to vote against the budget and bring down the Likud government," Sharon said.
"I call on you to use your influence with the men and make every effort to make sure that the Likud does not fall because this group has announced it will vote against the budget when it is presented," he added.
Several opposition parties have said they would vote against the budget, but are expected to change their position at the last minute if opposing the spending plan would mean bringing down Sharon and delaying the Gaza withdrawal. If he wins last-minute support from the opposition, Sharon could survive without the Likud rebels.
Under Sharon's plan, Israel will remove Jewish settlements from the Gaza Strip and four more from the northern West Bank. The opponents bitterly oppose conceding land to the Palestinians.
On Thursday, Sharon began a series of meetings with undecided lawmakers, attempting to convince them to support the budget.