All four candidates in the Kadima leadership contest want their party's primary to be held as soon as possible, but want the general election as close as possible to its scheduled date of November 2010, senior sources in the party said Thursday. Kadima and Labor authorized a deal Wednesday requiring Kadima to hold its primary by September 25. But the negotiators said that date had been chosen symbolically, because it was the final Thursday before Rosh Hashana. In consultations with Kadima's steering committee, the candidates recommended holding the race at the beginning of September. Any earlier would be problematic, because many party members are away during the summer months. The winning candidate would then seek to depose Prime Minister Ehud Olmert and form a new government as soon as possible. In closed conversations, all the candidates have expressed interest in forming a new government rather than going to a general election immediately. This would allow them to prove themselves and gain stature ahead of a race against the former prime ministers who head Likud and Labor, opposition leader Binyamin Netanyahu and Defense Minister Ehud Barak. Shas is expected to raise its price for remaining in the coalition and avoiding elections after a Kadima primary. However, a source close to one of the candidates said it should not be too difficult to form a new government, because "the lesson of this week's canceled vote on the Knesset dispersal bill is that MKs will do anything to avoid losing their jobs." The Kadima leadership race began in earnest Wednesday after the Kadima steering committee took steps to initiate the primary. Spokespeople for the candidates said they were focusing on registering as many people as possible in a membership drive that is likely to finish at the end of July. Olmert's associates said he would not decide whether to run in the primary until after the July 17 cross-examination of the main witness against him in his most recent corruption case, American financier Morris Talansky. His associates said he also had not decided whether to try to remain prime minister after the primary if he did not run. Kadima council chairman Meir Nitzan, who is close to Olmert, said he would recommend that the victor become Olmert's top deputy until the next general election. A source close to one candidate said that if Olmert tried to remain prime minister after the primary, there would be an outcry in both the coalition and the party that would force him to step down. A Dahaf Institute poll of Kadima members published in Yediot Aharonot on Thursday found that if the suspicions against Olmert were found to be less grave than currently thought, he could win reelection as party head. According to the survey, Olmert would win the race in those conditions with 30 percent, followed by Foreign Minister Tzipi Livni with 26%, Transportation Minister Shaul Mofaz at 19%, Public Security Minister Avi Dichter with 9% and Interior Minister Meir Sheetrit at 6%. If Olmert did not run in the primary, Livni would win with 40%, but Mofaz would get 30% - up from 25% in a poll taken by the same company just three weeks ago. Dichter would win 12% and Sheetrit 9%. A Ma'agar Mohot poll on Israel Radio found that 42% of Israelis supported the deal between Likud and Labor that delayed the next general election, while 36% opposed it and 22% had no opinion. The poll found that a majority of Israelis believed Barak had "surrendered" to Olmert and not the other way around. Also Thursday, Barak held a rare meeting with his Labor nemesis, former party chairman Amir Peretz. Both sides said the meeting went well and that they discussed security issues and not politics.