Peres is 89 going on 90 so how long can we practically expect him to be around for? Do was want the PM who is going to die in office, ulnles Livni wants to be his deputy and use that to rebuild her own image and if she is lucky Peres will die in office and she become the next PM by default. If Peres wants to do the best thing for the country rather than personal ambition or Livni's ambition ( she wouldn't be doing this unless there was something in it for her ) then he will tell her no thanks. Long term it might even benefit Likud because to stand Peres will have to form his own party because both Kdima & Labor have held their primaries so he will be running against Labor & Kadima as we'll as Likud and this will be a party built around a single man so when he does have to retire from politics or he dies the party will be without the leader they all voted for and it will eventually implode the way Kadima has. Originally Kadima was Sharon's baby and it wasn't going to resemble anything like it does today and Olmert got elected on a sympathy vote for Sharon then as a mixture of Olmert doing a lousy job and the party loosing its direction its expected to go from being the largest party with 29 seats down to 5-6. Kadima was a here today gone tomorrow party and any party built around Peres will be the same. If Livni were to try and boost support for Labor then she would be strengthening the only party with the muscle to defeat the right long term. Do it this way then whilst Peres is in charge there will be unity but once he has gone there will be chaos.
Motorcyclist in his 20s dies after crashing near Gedera (Haaretz)
from the article: Tzipi Livni pushing Shimon Peres to run for Israel's premiership