Eventhough todays press shows all muslims as terorists or extremists, i believe most muslims are against to Sharia Law.
Take Turkey for example; The country has %98 muslim population yet they are secular. Well i know Turkey is the only secular islamic country but it also has one of the highest populations in the area.
We see more and more revolutions (as Egypt. Libya, Tunisia etc.) against monarcy and sharia everyday. Those people are sick of Sharia law and they dont want it. But they dont have saying in parliament.
Quran is not a governmental system (regime). Quran is a book of a religion (Islam).