Given:
Where the id = datepicker tells the javascript to attach all the datepicker code to
It's not a good idea to bind a datepicker to an ID. better is to give it to the class (in asp.net: CssClass) then, multiple inputs can have datepickers. so in short, bind the datepicker to a class. This also fixes your asp.net problem about the ID's
then in your jquery selector:
$(".datepicker").datepicker()