Why would you think there's some line the military wouldn't cross? Is there something in their recent history which suggests they have this kind of line? These are the guys who were photobombing themselves torturing people at Abu Ghraib.
There might be a small subset of soldiers who would be a bit mopey about it, but these are American soldiers. They'll do what they're told and pass of the moral implications of that to someone else while not particularly caring.
There was a report on the radio that at least a few generals have chimed in saying they would NOT obey an illegal order. In this case, they were specifically talking about cheetolini's threat to take out cultural sites.
It will be interesting to see what happens (at least what we, the public hear about) if something like this does occur. You may have noticed, though, that quite a few high ranking Pentagon officials resigned in the week prior to the assassination. So maybe the 'good ones' are leaving. :/
