The Little Girl Voice is an informal name for a vocal trait in adult women that is caused by psychological trauma . Women that are affected speak in a higher sounding, child-like pattern, usually in a manner similar to the age at which they suffered the traumatic event.
She spoke in this affected style specifically to recall the image of a poor innocent teen in the minds of the audience. It worked on the Democrats because they wanted it to work, just as a hypnotized person willingly submits to the hypnotist.