Egypt has a dilemma: its politics are dominated by democrats who are not liberals and liberals who are not democrats.
This is a pithy and elegant way to put things that Samer Shehata has used in this NYT op-ed, but I think it's inaccurate. A lot of it depends on how you use the words "democrats" and "liberals". The meaning of democratic is wooly in the age of universal human rights, because it does not always take into account cultural specificities. Many would say that even if fairly elected a government is not democratic if it does not take into account minority rights, gender rights, even gay rights. Likewise "liberals" can't be called liberals if they want to return to the old security state that existed under Mubarak (esp. towards Islamists).
The dilemma facing Egypt is that it's a limited, electoral democracy whereas many want it to be a republic. The difference being that in a republic the individual has guarantees in the context of a socio-political compact, whereas in a democracy the minority has little if any voice. Egypt is formally a republic, and has been since 1956, over several iterations of a compact (one that failed over the 15 years). It might have turned into a more democratic republic after 2011 except the new social compact was left to elections. Because elections are not very accurate indicators of national sentiment (because of variety in electoral systems, the importance of electoral strategy, etc.) and the voting public has still mostly few lasting allegiances in post-revolution Egypt, this was always a bad idea. A lot of people have changed their mind.
However Egypt comes out of this crisis, hopefully a republican pact — hopefully based around a bill of rights — will form a more stable base for its political system.