Chirac has told his people that a "Yes" is vital for France and Europe.
He is aware that many people are voting Non because they don't like him. If his real priority is the interests of France, he could offer a conditional resignation:
"If your vote Yes, I will resign on Tuesday morning."
This would almost certainly be enough to swing enough No votes into the Yes camp to win the vote. (Unless, of course, there are a significant number of Chirac supporters so horrified at the prospect of his departure that they would decide to vote No. Somehow I doubt that!)
But what are the chances of any politician being prepared to make that kind of self sacrifice?