Somewhere in Mother Jones's impossible to navigate archives, Brad Plumer writes:
it might not be the end of the world if democracy in the Middle East gave rise to Islamic governments, as many have feared. Eventually, these leaders have to keep the country running smoothly, and they need to answer to voters. An overly-zealous and incompetent government could well turn people away from religion altogether, or promote the development of a secular society, as we're seeing in Basra.
That's a pretty undercovered point. So long as religion is kept out of the public sphere, it gets to play in rhetorical fantasy lands and promise all sorts of utopias for the glorious day when it takes hold of the government. That, for instance, is exactly what what Ayatollah Khomeini used to fuel the Iranian revolution. Religion, which by nature is conceptually unmoored from the terrestrial realities that constrain (if only slightly) the promises of most political parties, can promise nothing short of paradise, and nothing more specific, which allows all aspects of society to project their own desires onto the moral perfection to come. Once the demagogues reach office and start restricting freedom, imposing Shari'a, and mishandling the economy, however, support drops fast. If we're dealing with a democracy that means the theocrats need to respond to popular opinion or lose power.
But that's a big if. Under democracy, it might almost be best for the Islamists to take power. Let them attempt faith-based economics in an already-ravaged economy and lose their public support. If the democracy is weak, however, popular discontent will lead the regime to oppress its people or, in the doomsday scenario, pick a scapegoat and distract their supporters by hunting down the Sunnis. Then you have civil war. So while an Islamist regime spending itself out and getting voted down would be great, it's not a chance that can be taken unless the democracy is independently strong or externally guaranteed, and I'm not sure Americans have the stomach for the latter.