According to this WSJ piece, Regime Seeks an Exit for Mubarak, one of the possibilities being considered towards solving the deadlock between President Mubarak and the Egyptian people is to make the president into a figurehead, a symbol of continuity during a proposed transition period, but completely stripped of executive powers. As to how that will play out remains to be seen.
But it seems to be a happy, well-conceived compromise. Perhaps a win-win for everyone. The arrangement seems practically prudent not only because of the chaos and turmoil but also because of the major security concerns in the Middle Eastern region that require stability within the Egyptian government. This compromise may give Mubarak the opportunity to tell his people that he gets their message (doing so will dignify his legacy), and that indeed it's time that they be made the sole source of all sovereign powers in Eqypt.
But a peaceful transition does take time. And so this proposed arrangement presents an opportunity for the people to show their common sense and practical understanding of the limits of power: that they have made their will known in the public square, and that they recognize that at some point they have to go home to attend to the business of everyday living. But they will leave the public square with a promise from their government that liberty and well-being are there for their taking, with nothing less than the rest of the world as their witness.
Egypt is the seat of one of the great ancient civilizations. It will survive this crisis with dignity.