Well considering the scale of the situation I do think it would be difficult but in this kind of moment life become cheap as terrible as it sound.
The world is about to die and the only thing our character can do is try to soften the blow. Morality and what is "right" become more and more confused as time goes on so anybody in this position of power need to became a machine otherwise feelings might cause more damage to the whole.
An example would be having having to chose between a children and a soldier. The moral thing to do would be to take the children but when you consider the whole situation, a soldier have the capacity to save more peoples than the children.
On the other hand the child is innocent and could grow up to become an efficient member of the colony so when it come down to it there is no good answers, only actions and reactions. And no matter what you chose peoples WILL try to use it against you and complain.