Hosni shoves back and sets his terms. He won't go without being burnt out. The revolution, if it is to succeed and political power Egypt wrested from his control and influence, almost certainly now requires that he be chased to the airport or the Sahara by the masses.
The problem is that this risks turning the revolution ugly. If the public doesn't keep the pressure up, the revolution's momentum may become uncoordinated, fractured, and thus lost. He's challenged the Egyptian public to follow through or go home, in effect turning it into a battle of wills. He kept them prone and obedient for 30 years, and perhaps he thinks he still might.
Perhaps he thinks that if they follow through, he'll go postal, and order his loyalists to draw as much blood as they can, thereby spoiling the chances for peaceful resolution and a coherence aftermath.
Or maybe he's just an old man trying to bluff his way to retaining power he's already lost.
The US has burnt its local strongmen before. Obama could do it again, and this time in a place where the local population is in popular uprising and holds the high ground. Those old neocons must be spitting acid. Then again, we know what tends to happen when the Americans try to dick around in other people's governments.
Ultimately, this is up to the Egyptians.