It was all a political and personal game. Indeed, each of them boasts that he can defeat Sharon - as if the issue is defeating Sharon, rather than making peace. He has no chance at all of winning this election if he does not present to the electorate an agreement with the Palestinians. Only such an agreement will bring the hundreds of thousands of Arab and Jewish peace-seekers to the ballot box, and without them he will lose. For him, peace is not a consuming passion, but a means to an end - winning the elections.
Common sense says no.
But one should not belittle the immense determination of a politician to survive when faced with disaster. Peace may use even a strange instrument like Barak. That's a faint hope - and blessed be the believer.