[I apologise for this not being particulalry satirical - maybe someone smarter than me might be able to develop some satirical ideas from it. But this is supposed to be the Chat Room, after all.]
I am struck by the similarities between Egypt now and Britain in 1688.
Given that modern ideas of electoral democracy were not the same in the 17th century, James II as the hereditary monarch of Britain was as legitimate a head of state as President Morsi is of Egypt. However like Morsi he attempted to rule 'absolutely', ignoring the wishes of many of the people, attempting to impose his religion on the country and unauthorisedly promoting many of his cronies to positions of high office.
This incurred the displeasure of the people as well as the army which mutinied and backed a popular peoples' revolution. These rebels, who incuded much of the nobility and other powerful people, invited Williamandmary to come over from the Netherlands and become the British monarchy, to replace James who fled.
OK, the Egyptian arrmy is not likely to split or to mutiniy; it is far stronger and is totally united. If it acts it will do so as one body, clearly and decisively. And neither the Egyptian people nor the Egyptian army are likely to try to import a new head of state from outside the country.
If the Egyptian army are smart, they will take power and give the non-Islamicist part of the population, say, 12 months to get their act together and form one united, credible opposiiton party, and then hold another general election.
But the lesson from both these episodes is: however technically legitimate your hold on office, do not try to impose your will unilaterally and do not piss off large parts of the population by totally ignoring their aspirations. There is more to running a democracy than just winning elections.
The only other alternative is to rule with complete ruthlessness and forgo any claim to democratic legitimacy: be an utterly despotic bastard like Gaddafi or Saddam Hussein - and piss off the entire world.
(In my not-particularly-humble opinion, of course.)