Yes, most of us do support the mission - any mission - once the battle has been engaged. Failure to do so means you want the mission to fail and to lose lives "in vain". That is not an option.
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More nonsense. Failure (interesting word choice since it is not obligatory) to support any particular mission does not mean, as you say, that it means that you want military lives spent in vain. I do not believe that you have supported every past use of our military or will support every future use of the military.