Some Game Theory and the Security Council
Let's assume a little economic game. Five players -- the US, UK, Russia, France, and China -- each hold a veto over military action by any player in the game. One, player, the US, decides that military action in Iraq would be valuable to the US. A few other players, such as Turkey or Kuwait, can choose to contribute or withhold valuable resources.
The other players might be better off after US action, and they might be worse off. In any event, if they are fully self-interested, they will ask themselves how they can get the maximum pay-off from the US for not exercising their vetos.
They might decide to join the US early (as the UK did), in an effort to influence the military campaign and subsequent reconstruction, or to establish an international legal principle that Kosovo is better than Rwanda -- that in appropriate cases, the nations of the world can use military force to stop a government from committing atrocities against its own citizens.
Or they might try to position themselves so that they are the last hold-out. Once the US has paid off every other player necessary to obtain UN approval, the remaining hold-out can demand any price up to the total value of UN approval to the US - the rest are sunk costs, and no longer affect a rational player's analysis. The players can try to be the last hold-out just by staying quiet (Russia and especially China) or by publicly assuming a position that makes it clear than no one is more opposed to UN approval than they are. (France).
I couldn't find a good econ link explaining this, but it seems like a variant of the railroad problem. If I am buying land for a railroad track (or a road, fiber-optic cable, etc.) and I buy land from everyone I need but you, I have given you the power to hold me up. If I'm smart, my contracts with everyone else let me back out of the deal if you don't sign, but if I want a route through your land and you're the last one, you can really stick it to me.
Now there are some things the US can do in this game. It can hint to the other players that UN approval isn't very valuable to it, which means they will sell at a lower price. It can try to keep each player confused about whether it has the approval of the other players. Finally, if the price is too high, it can go ahead without UN approval.
I guess where I'm going is that the UN veto structure is unworkable to this kind of humanitarian intervention. It does a good job of avoiding a world war, because as long as the permanent members have no opposition to a conflict, it's unlikely that we'll ever see the kind of chain of alliances that led to the first World War. However, the Security Council model is lousy for this situation -- where the US wants to depose Saddam, the French want to lift sanctions but aren't willing to go to war over it, and the other nations are mostly looking to see what's in it for them. Under those circumstances, each nation is likely to hold out for the biggest pay-off it can get, and ruin the whole deal in the process.