May 3 (Reuters) - Israeli Prime Minister Ehud Olmert appears to have survived an initial challenge to his leadership from within his Kadima party over the findings of a commission criticising his handling of last year's war in Lebanon. Following are the potential obstacles that Olmert still faces and details of how these could play out: *A large turnout at a protest rally in Tel Aviv on Thursday could renew public pressure on Olmert to resign or reignite efforts within Kadima to persuade him to step down. Under party bylaws, he cannot be dismissed as Kadima's leader. Organisers of the demonstration seeking Olmert's resignation said they expected 100,000 to 150,000 people to attend. Should Olmert step down, he would stay on as caretaker prime minister until a new government was formed, a process that could proceed without a national election and set the stage for his successor as Kadima leader to become the next premier. Frontrunners in Kadima to succeed Olmert are Foreign Minister Tzipi Livni and Deputy Prime Minister Shimon Peres. *Olmert's government could lose its majority in parliament, paving the way for an election, if the largest coalition partner, the Labour party, decided to bolt after a May 28 leadership contest. Such a move would be risky for centre-left Labour because opinion polls predict former Prime Minister Benjamin Netanyahu's right-wing Likud party would win an election if it were held now. The frontrunners in Labour's leadership race are former Prime Minister Ehud Barak and Ami Ayalon, a former admiral. Opinion polls show either could defeat the incumbent, Defence Minister Amir Peretz. *Olmert could survive until the Winograd Commission issues the second half of its report, expected to be released in several months' time. The panel has hinted in the findings published this week that it might ultimately recommend Olmert resign.
