In terms of dramatic conventions, when the President says "What you are asking me to do is declare martial law", it clearly means he's engaging in hyperbole. If the soldiers really were asking him to declare martial law, then the President would have no need to spell this out.
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It's much more likely that it is martial law and that the President spells it out not so much for the soldiers as he does for the audience. The same way a villain tells the good guy what he's planning to do. You don't really think that bad people always tells the good guys what they are about to do before they shoot them do you? Yet it's something we very often see in fiction. It's a way to make sure that the audience is informed of what's going on.