If Ariel Sharon does not return to office, the Middle East peace process will be significantly affected by the absence of such a major figure - but it is not the only problem it is facing.
The Bush administration may pin its hopes on Ehud Olmert
There is uncertainty on the Palestinian side as well.
There is chaos on the ground in Gaza and Hamas is threatening to make a strong showing in the parliamentary elections due on 25 January. If Hamas should win, Israel would not negotiate with it, given its aim of destroying the State of Israel.
The elections themselves are even in doubt because of Israel's refusal to allow Palestinians in Jerusalem to vote.
There are therefore a number of factors that could leave the leadership of the Palestinian Authority President Mahmoud Abbas undermined.
So two things have to happen before we know the chances of seeing negotiations resume.
The first, of course, is that an Israeli leader has to emerge if Mr Sharon does not come back. This will be determined in the election on 28 March.
The second is that the Palestinians must resolve their uncertainties and present a coherent negotiating front.
If there are to be no talks, the current Israeli policy of reshaping the map by unilateral moves will probably be the pattern for the immediate future.
And the unstable mix of no peace, no war will carry on, with flare-ups from time to time.
Continuing Sharon's policies?
The Bush administration, in casting around for a way forward and a way of furthering President Bush's stated ambition to see a state of Palestine alongside Israel, is likely to latch on to acting Prime Minister Ehud Olmert.
Mr Olmert, an ex-Likudnik and mayor of Jerusalem, led the way for Mr Sharon in presenting ideas for a withdrawal not just from Gaza but from wider areas of the West Bank.
In an interview with the Israeli newspaper Yedioth Ahronot in 2003, Mr Olmert made clear that he too believed in the unilateral delineation of Israel's borders - to be determined by a pullout from Gaza and most of the West Bank, but not including a return to the "Green Line" that defined the border between 1949 and the war of 1967 and also not withdrawing from Jerusalem.
"Through such a move we will define our borders, which under no circumstances will be identical to the Green Line and will include Jerusalem as a united city under our sovereignty," he said.
That will presumably remain his policy if the Kadima party he helped Mr Sharon found wins the most seats in the March elections and is able to form a coalition (as all Israeli governments must do given that the divisions in the country are reflected in the Knesset by proportional representation).
Missing from this policy will be Mr Sharon's personality and panache.
Ehud Olmert is no mean politician but he is by no means a proven national leader and he lacks the military record, the passion and the public impact of the man he has followed.
Ariel Sharon has been a key player in the Mid-East peace process
"There are many hurdles to overcome before peace talks can resume," said Danny Shek, a former Israeli foreign ministry spokesman and now chief executive of Bicom, the Britain-Israel Communications Centre in London.
"The first is, will Kadima win if Sharon goes? Will it prove to be a one-man party or not? I think it is not, but the election will decide.
"If it can form a stable centre-left coalition with Labour there will be the motivation to continue the peace process.
"Ehud Olmert was more ambitious than Sharon, two steps ahead of him. So the concept should continue under his leadership. There are vast areas of flexibility before the red lines - no return to the '67 borders, no giving up of the big settlement blocs and no division of Jerusalem - are reached.
"The other hurdle is the Palestinian election, if it even takes place. Hamas does not want Israel to exist and even if it changes that would be in the long run. So right now, only once both elections are decided will the world be able to assess what might happen next."