Most Iraqi's I have meet really want us to stay. On our old FOB there was this one big fat old lady we all called Jabba the Hut. She would always let us use her roof for night OPs. She would make us tea and give us bread and anything we wanted really. When we told her we were leaving she was in tears. She said the Iraqi Police and Army is corrupt and incompetent and little more than a group of well paid thugs. That seems to be the common sentiment from most of the folks I talk too even those in the Iraq Army which I work with daily.
Granted, that's all anecdotal but it appears to be the uniform opinion.
While anecdotes might not equal hard data, what you describe is in fact a trend that's been coming from most who have talked with individuals there in Iraq. I'll attempt to offer an interpretation of what this means in a generalized cultural context, and you can let me know if it sounds even remotely applicable based on your own experiences with folks in the towns and cities there.
On the whole, most of the people you're going to run into as far as the civilian population in Iraq aren't going to want the US military to leave. Compared to the Iraqi forces, both police and military, they generally feel safer with the US forces around. You mentioned the accusations of corruption already, and even describing it as corruption is putting it lightly as far as I'm aware-- I've heard local police and politicians described as sanctioned sectarian fighters and thugs wearing suits (though not those exact words). The average people not only have no reason to trust them, but also have every reason to believe that they aren't going to be appreciably different from the previous government opportunists. But the main reason they want the US military to stay is because they prefer to not get shot or blown up, and can't afford to go into Jordan or elsewhere like many others have. And on the other side of that, they're not really all that interested in a US-style government, especially not if the US is the one telling the government what to do. What they feel isn't resentment at the US government, but what the people there most want is to be left alone by outside forces, not to make a politicized statement that some party in another country can use to claim is in support of their positions. Granted, the environment there in many neighborhoods would be considered *%&#-ed up by American standards, but environment aside they just want similar things that people in the States want-- clean water, a way to make a buck, food for their families, fewer bullet holes in their walls... the basics. They want simple stuff like basic safety on the streets, the ability to hold a job, and the staples of what could be considered modern living. For the most part, they don't care if it's the US military or their own military and police providing that protection for them to try to have it, so the default is that they prefer the US military they know has the might as opposed to the local police and military who have so far seemed no better than the militias from three years ago.
How's that in your opinion, foxholeatheist? It's a bit more descriptive than what you said, but since your words were so similar to other accounts I've heard I added them together.