Livni's chief rival, MK Shaul Mofaz, told The Jerusalem Post at the Knesset that he had "a solid block of support" for changing the party's constitution.
At the meeting, Mofaz will propose that if Kadima's leader isprime minister, a leadership race should be held six to nine monthsbefore a general election, but if she is not, it should be held nolater than 16 months after the last election, which would mean aprimary in June.
"Most people in the party want a compromise and I am confident that there will be one," Mofaz said.
MKs Avi Dichter and Meir Sheetrit both said they wanted theprimary in 2010, but closer to the end of the year so as not to putundue pressure on Livni. Dichter reportedly reached a deal with Mofazto work together to advance the race.
The Kadima leader lashed out at all three of theMKs she defeated in an interview with Israel Radio's Yoav Krakovskybroadcast on Friday.
"The time for the primary will be based on the interest of theparty winning the election and not the personal desires of people whodon't accept the results of the last election and are demanding arematch," Livni said.
A source close to Livni added that "the only decision that will be passed is the decision that she wants to be passed."
Kadima council chairman Haim Ramon, who is loyal to Livni, saidthe primary could be moved up from three months before the next generalelection to nine months before. Livni's critics scoffed at Ramon'ssuggestion, saying that since no one knows when the general electionwould be, if it were advanced, the primary could not be held more thanthree months before the election even if a nine-month rule was set.
MK Shlomo Molla, who is a strong Livni supporter, said he saw no reason why the primary should be held before 2013, if at all.
Another Kadima MK said the main consideration should be whetherPrime Minister Binyamin Netanyahu would renew the 10-month settlementfreeze after it expires in September. He said it might make sense towait with the primary until after it is clear what Netanyahu will doand whether it would cause right-wing parties to bolt his coalition andperhaps lead to the advancement of the next general election.
MK Tzahi Hanegbi, who heads the House Committee, said he wouldmake a serious effort to bridge the gap between Livni and heropponents.
It is possible that a decision will not be made on Thursday.Whatever passes in the committee would need to be brought to Kadima'sfaction and council for further approval.