Iran in 1979 had a revolution that was supported by a broad coalition. Then the Islamists took over and monopolized power. The same happened with the French revolution and the Russian revolution. There is even a saying that "a revolution eats its own children" - meaning that the revolutionaries of today may tomorrow be sidelined and imprisoned by their more radical brethren.
For this reason the suggestion by US envoy Frank Wisner that Mubarak should guide Egypt through a transition to more democracy makes some sense. However, there is no way to be certain that Mubarak really delivers and not goes back to his old ways as soon as he sees a chance. Abolishing the Mukhabarat, Egypt's infamous secret service might be a good start.
Radicalization of the revolution might happen most probably when the situation is not clear. Mr. Mubarak has had his chance and he has missed it. Now the main task should be to establish a broad coalition that can guide Egypt towards a more democratic future. When they set clear goals at the beginning the chance for radicals to take over will be the smallest.
Postscript: After protests the US retracted a bit from Wisners position, but not much. It appeared that Wisner - some years ago ambassador in Egypt - is working now for Patton Boggs, a lobbying firm that has the Egypt government and military among its customers.
Postscript 2: Here is a plea for a constitution and an orderly transition.