I know the spirit you meant in a one-liner. And you probable know well what I am about to say. So forgive me, I am feeling earnest.
1) The G.A., in today's climate, would probably produce something worse that the S.C. (and, of course democracy is a vote by people not governments). We have to remember what a new world it is and that only a handful of governments from large countries will oppose the U.S. if their interests are not immediately threatened. (To be precise the G.A. would produce a resolution larded with lots of fine language as a cover, but would leave the specific levers of power in the hands of the U.S.)
2) If one wants to be constructive (a very relative term, given the situation) then one has to try to pry away those levers and give them to a fair and balanced group of Iraqis. Perhaps more accurately, one has to leave them untouched until such a balanced group of Iraqis can emerge from their internal processes. (I know I give no definition of fairness and balance among Iraqis in such a fluid situation, its too long an issue.) Although these levers of power are the only bait to coax the different ethnic and religious groups into a sense of mutual accommodation and respect, these levers of power are being irretrievably given out as we speak and the concomitant policies are being announced (two key economic policies in the last two days: foreign ownership and J.P. Morgan as the new Trade Bank). This forecloses incentives for compromise.
A "fair" Occupation Government (U.N. or otherwise) and its Iraqi participants would focus on humanitarian assistance and 'down the middle' rehabilitation, like getting the infrastructure up and running. This usually takes a few years and lots of money - it should keep people busy enough. The important institutional issues such as public\private ownership would not be dramatically decided (contrary to the Geneva Conventions) nor need they be. Likewise efforts would not be made to tip the power balances within each community among local leaders and broker community-wide blocs among them (much of what is now being called "encouraging local governance" amounts to this manipulation).
3) Sometimes the "U.N." has acted this way (Cambodia, Namibia). More recently, less so. IMHO there is no Arab or regional institution capable of playing this role (including the Arab League) unlike Africa, Lat America or Asia. The U.S.'s opening proposal is just a U.N. military role in supplying troops to U.S. leadership. The French replied, as they have before, calling for a political role (but this could degenerate to just spreading out the foreign contracts). The specifics of the mandate and arrangements are key, but these are not things around which one can mobilize a mass movement. In short, it is important not to be drawn into a superficial debate about a "U.N." occupation or not. One needs to keep people focused on the principles as our goal - they are the honorable and traditional principles of self-determination and non-interference. Same old struggle, as they say.
Paul