The large number of Jewish holidays this month have cut into Livni's negotiating time.
Livni has already won an initial agreement from the Labour party, lead by Ehud Barak, the defence minister, to join a coalition under her leadership.
However, her efforts to attract Shas, which is making a number of demands, have so far proved fruitless.
"Shas ... know that Tzipi Livni really needs them in order to become prime minister and to form, not just a strong government, but a legitimate one"
Sherine Tadros, Al Jazeera correspondent
"The Shas party has an incredibly important bargaining hand in this whole process," Sherine Tadros, Al Jazeera's correspondent in Jerusalem, said.
"Shas is not afraid of early elections being called and knows that Livni really needs them in order to become prime minister and also for her to form, not just a strong government, but a legitimate one.
"Israeli public opinion really needs to see a religious party, such as Shas, in order for them to back any government that Livni puts forward," she said.
Shas, which has long billed itself as a party that represents Israel's poor, has been demanding increased government spending of about $270m on social welfare as a price for joining a Livni-led coalition.
For Barak, a former prime minister who readily acknowledges he lacks enough public support to regain the office if a national election was held now, the power equation is simple.
"If a government is established, there won't be elections," he said on Army Radio.
"I know the truth is that I don't have the political backing to be prime minister. I had the option, which I have chosen, to be a senior partner to Tzipi Livni."
With Labour in her corner, Livni would control 48 of the 120 seats in parliament.
Shas's membership would boost that number to 60, a wafer-thin coalition but enough to stop the opposition from toppling her government in no-confidence votes.
Winning the support of smaller factions, such as the Pensioners party, with seven Knesset members, and left-wing Meretz, with five, would give Livni a stronger mandate to pursue policies that include peacemaking with the Palestinians.
Negotiations between Kadima and Shas are likely to be stepped up, amid speculation that Livni intends to present a government when parliament reconvenes on October 27 after its summer recess.
Without Shas, she could form a minority government relying on precarious support from outside the coalition of left-wing and Arab parties wary of a national election that opinion polls show Benjamin Netanyahu's right-wing Likud would win.
"She could go to the Knesset [to ratify a government] with the seats she already has, but she believes she can do it in the end," Gil Messing, a Livni spokesman, said.
Olmert remains in office in a caretaker capacity until a new government is formed.