Livni, who has billed herself as "a different kind of leader" unwilling to engage in backroom deal-making, said she would not make the political and financial concessions demanded of potential coalition partners. One small conservative party, for example, would back Livni as prime minister only if she dropped her emphasis on Palestinian peace talks, she said.
She preserved her image as "Mrs. Clean," but lost the top post.
Kadima lawmaker Eli Aflalo likened her style to "trying to fish without getting wet."
"There is no 'different politics,' " said Aflalo, who has threatened to quit the party. "It is what it is."
Aflalo and others also complain that Livni is too focused on her image and popularity, can come across as arrogant and fails to take opposing viewpoints into account.
She has been criticized for failing to clearly articulate Kadima's platform and for not being more critical of the government's policies, though Netanyahu has reduced the opportunity by embracing many of Kadima's principles.
Livni's supporters say the attacks smack of sexism and ignore her personal appeal to voters. She's a former spy with Israel's Mossad. Her parents met while working together in the Zionist underground before Israel was founded.
Without Livni at the helm, Kadima would lose much of its support, experts say.
"The ballots that voters cast for Kadima were really ballots for Livni," said Merav Parsi Zadok, a political and media consultant. "She's popular and it's personal."
Livni said she's confident she and Kadima will survive the current challenges.
"I'm not naive," she said. "The public wants to see something else. There is a need to keep the alternative of hope."
But she added that she would not hesitate to support, or even join, the current government if such a step were needed to end the conflict with the Palestinians.
"Even if it were the last thing I did in my political life, I would do it," she said. "I'm in politics in order to end this conflict. This is the most important thing."
Sobelman is a researcher in The Times' Jerusalem Bureau.