I think if the death toll had been in the hundreds or thousands during the initial invasion of Iraq public support for the war would have dropped like a stone.
Our troops did as well as they did because they are the most highly trained and capable military force in the world. It has nothing to do with the "current administration" or his leadership.
Our soldiers fight and live because they are trained to do so. Not because President Bush is "leading" them to do so.
Well, it does have to do with the administration's willingness to speak firmly and follow through with more than more hollow rhetoric.
Granted, the administration had nothing to do with the mission or its successes directly, but that mission would not have taken place had our military not been put in motion by those who were willing to allow it to perform its function when needed.
I don't doubt your assessment of public support. Just note that Saddam Hussein mentioned our withdrawal from Somalia over the death of 17 troops. He essentially estimated the US's fight to be equivalent to Amnesty International's.