In spoken English, object pronouns are also used as emphatic or referential pronouns.
For example, I typically think of myself as "me," and a group including me as "us." We use these emphatic or referential pronouns in any stand-alone statement (i.e. one without a verb), such as a quick answer to a question.
Thus "who wants to come?" You could say in response "Me." "Us." "Not us." or "Her" or "Not us, but maybe them." (note that with "you" there is no ambiguity since the subject and object pronouns are the same.) Saying "I" or "we" or "they" or "she" is ungrammatical. Saying "I do" or "they don't" is fine but is not what most English speakers would do.
In prescriptive grammar, this is frowned upon. Hence, for instance, you can find scorepads for card games labeled "we" and "they." In my opinion this style of speech sounds very unnatural. Unless you are writing a formal document, you should aim to talk like the child in the movie, if your goal is to sound more like a native speaker.
Similarly, in response to "Who's there?" "That's me." Or when a stranger calls you on the phone and asks "Is Sarah there?" If you are Sarah, you say "that's me." (Prescriptivists will tell you to say "this is she," but this again sounds extremely formal.)