You could fill the default value through javascript as seen here: http://jsfiddle.net/7LXPq/
$(document).ready( function() {
var now = new Date();
var month = (now.getMonth() + 1);
var day = now.getDate();
if (month < 10)
month = "0" + month;
if (day < 10)
day = "0" + day;
var today = now.getFullYear() + '-' + month + '-' + day;
$('#datePicker').val(today);
});
I would probably put a bit of extra time to see if the month and date are single digits and prefix them with the extra zero...but this should give you an idea.
EDIT: Added check for the extra zero