Thus far the Americans don't seem to be hiding or censoring their attacks and casualties. But the drip-drip of ambushes and American dead and wounded is clearly taking its toll. Also, bluster from Bush about "bringing them on" when he isn't the one having to patrol Baghdad in hundred-degree heat might help more and more Americans to draw appropriate conclusions about him.
Perhaps the US authorities will be tempted to cover up their casualties in future because it is politically sensitive.