Labor's leadership election looms in May and current leader Amir Peretz looks extremely vulnerable. When the Kadima-Labor coalition took power, some felt it was a good move on Peretz's part to take the Defense portfolio, since he couldn't get Finance. He can establish himself as a competent minister and not take the heat for tough budget and taxing decisions, it was said. Well, Olmert and the IDF screwed that up for him, looks like...
Now Peretz faces opposition from several fronts--it's only early January, but Peretz has been in trouble since Lebanon. Former Labor leader Ehud Barak is jumping back in as a Labor establishment candidate and is supported by such long-term Labor figures as Benjamin Ben-Eliezer. Ami Ayalon, former head of the Shin Bet, is a candidate, backed by Avishay Braverman. Both are relatively new to electoral politics but have been prominent figures for a longer time. They appear to be pragmatists without the baggage of Barak. Finally, there is Ophir Pines-Paz, the principled ex-cabinet member who left government over the appointment of Yisrael Beitenu's Avigdor Lieberman to a ministry.
At this point, Ayalon and Barak appear the front-runners. Of all of them, Ayalon seems to most represent the perspective of a social-liberal party, which Labor now is; Pines-Paz is too left, and not really a major figure, while Barak seems more to the right, and still very vulnerable to criticism, though not immune to bouncing back, due to the general low standing that all public figures today enjoy. Personally, I saw Ayalon speak while in college, as he was doing a tour on his citizens' initiative with Sari Nusseibeh, and while he certainly held back for what I believe to be public-image concerns as well as very real personal beliefs, I believe he is sincere (not to be making any comparisons with Ehud Barak...).
What does this mean for the peace process? Ehh... essentially nothing. Unlike past times when it's been asserted that "there is no Palestinian partner" except that there really was, Israel now through its destructive policies has managed to self-fulfill this prophecy. Now there really is no partner, at least for now--not because nobody will negotiate, but because the legitimacy of whoever does it will be questioned by a majority. (Given that Israel controls the process overall, this is not an insurmountable obstacle if they really wish to take action; but the problem is that the Palestinians must present a united front to challenge them at the table, or the Israelis simply will not move due to domestic political concerns).
As for Ehud Olmert... check out this great post for how he's doing.