A class for animating messages as feedback to the user
It looks really good! The only bit I don't like is the nested ifs, but I'm really nit-picking.

       if (hide) {
            if (obj.input_element) {
                obj.input_element.removeEventListener("keypress", obj.enter);
            }
            obj.cover_element.style.display = 'inline';
        } else {
            if (obj.input_element) {
                obj.input_element.addEventListener("keypress", obj.enter);
            }
            obj.cover_element.style.display = 'none';
        }


Maybe....

obj.cover_element.style.display = hide ? 'inline' : 'none';
if (!obj.input_element) return;

if (hide) {
   obj.input_element.removeEventListener("keypress", obj.enter);
}
else {
   obj.input_element.addEventListener("keypress", obj.enter);
}


Putting the return value at the start, instead of protecting both blocks from it being null, makes it slightly more understandable. But I still don't like that section much.