"I've heard the US might stay 2 years in Iraq, or until democracy is established; What will Iraqis think of it?"

Well, one thing which is known, a mob on the street is not what Iraqis think. As soon as we can determine what the Iraqi think, they will have a democracy- and then we are outa there [so it's a moot question].
What's probably more significant is what Arabs in other countries think- and again this isn't "expressed" by some mob- or even a polite demonstration, but rather by a dialogue among people. In a real democracy a protest can be one result of dialogue- usually after other types of communication has failed.
The current Iraqi protests are about the same level as fans in a football game- fairly meaningless. Other than there is some people who have nothing better to do with their time. And riots are going to delay any US departure.
If Iraqi want the US out of Iraq as fast as possible than they should stop walking and begin talking.