I agree with you but let me ask you this. Republicans got smoked in the '06 mid-term elections and the familiar reframe was the American people want a different direction in the war. If it was not pulling out what do you think it was? (not a rhetorical question nor attempting to ask it in a condescending tone).
I think most Americans want us out of there. I think there is probably broad disagreement on how that exit should come about, though; I think '06 was about wanting a competing voice in the government to counter what was being seen more & more as a failed policy & failed management by the admin.
I think that most Americans would not support cutting off funding; I don't think that's what they had in mind with the '06 election. I think that most Americans were hoping that the admin might actually work with the new majority on a compromise plan to get us out of Iraq, or start us down that road.