Here is a polling of Iraqis from about a year ago.
http://www.globalpolicy.org/security/issues/iraq/resist/2007/09bbciraqipoll.pdf
Of particular interest: questions eight, eleven, twelve, fourteen (the section on the US), eighteen, nineteen, and twenty-one.
The basics:
48% of Iraqis said that Coalition forces have done a "very bad job" at carrying out their responsibilities in Iraq. Additionally, 32% selected the less-severe but still negative "quite a bad job." Only 18% were split between "quite a good job" and "a very good job."
53% of Iraqis said they strongly oppose the presence of Coalition forces in their country. An additional 26% said they "somewhat oppose" the Coalition being there, adding up to 79% of the population saying that they aren't thrilled to have us there. Only 21% of the population expressed support of the Coalition being there.
47% of Iraqis said that they wish for the United States to leave now. 34% said that they wished for the United States to stay until security is restored. 10% said they wanted the US to remain until the Iraqi government is stronger. 7% said they wanted the US to remain until Iraqi security forces can operate independently. And 2% said that they wanted the US to remain in general but leave eventually. Meaning that 47% wish for us to leave, and 53% want us to stay.
Interestingly, a higher percentage (21%) blame Al Qaeda for the continuing violence in Iraq than blame the US (19%). Additionally, the Iraqis aren't terribly positive about their own futures post-occupation:
35% said that the US withdrawal would make full-blown Civil War more likely; 65% said that it would either make Civil War less likely (46%) or wouldn't have any effect on the situation (19%).
46% said that the US withdrawal would make it more likely that Iraq would become a base for international terrorists. 54% said it was either less likely (40%) or wouldn't have any effect on the situation (14%).
46% said that the US withdrawal would result in Iran taking control of parts of Iraq. 53% said it was less likely (29%) or wouldn't have any effect on the situation (24%). 1% said they didn't know.
Only 9% said that the US withdrawal would lead to increased violence in Kurdish areas. 89% said it would be less likely (45%) or wouldn't have any effect on the situation (44%). 2% said they didn't know.
So yes, the majority want us to stay for one reason or another, but that majority is shrinking. Given these figures (which I hadn't seen up until now) I would like to revise my earlier statement. Seeing as 63% of Iraqis polled said it was wrong for the Coalition to invade, it seems my previous statement about them being okay with the invasion but not the occupation was flawed.