There are many forms of democracy and our form of "representative democracy" is just one of them, it is no more the will of the majority any more than many dictators in the Middle East were.
The reason democracy cannot work in the Middle East is Islam, it is a very political religion that has a tendency to create extremist groups who will force their views upon others using intimidation and terrorism. So even if only a minority supported an Islamic state, their influence would be greater as we have seen throughout the Arab Spring.
It is not a coincidence that countries like Turkey, Libya and Egypt are the most modern predominantly Muslim nations and they are/were secular. Islamic law is very old and cannot be amended, so it seriously inhibits a countries progression - socially, culturally, economically, politically. Religion has no place in politics in the 21st century, yet all the political unrest were hear of in the Middle East is driven by it. The only way this region will see peace and progression is through secularism, because before it achieves that it cannot achieve democracy.