Your code should work.... are you including:
<script type="text/javascript" src="jscolor/jscolor.js"></script>
<script>
var bgColorPicker = new jscolor.color(document.getELementById('bgColorChanger'),{});
document.getElementsByTagName('BODY')[0].style.backgroundColor = '#' + bgColorPicker.color";
document.getElementByID('bgColorChanger').value = bgColorPicker.color;
</script>
before running the scripts?
<input id="bgColorChanger" value="" />
Will fill in the input value for you.