Edit: OP changed question.
var start = new Date(2013,11,19);
var end = new Date (2013,11,20);
db.collection.find({dateTimeField: {$gte: start, $lt: end}});
Thanks to gilly3's comment on OP highlighting: http://cookbook.mongodb.org/patterns/date_range/
Maybe there's something I'm missing since you're using mongoose... but:
var dateTimeStr = '2013-11-19T00:10:00-08:00';
var dateTime = new Date(dateTimeStr);
var formatted = d.getFullYear()+'-'+(d.getMonth()+1)+'-'+d.getDate();
The date-time value you have is a standard ISO 8601 which is parsable internally by the Date object.
I'm also not sure why you have a date-time stamp stored (or being fetched) as a string. MongoDB has the ability to store a Date object.
See Where can I find documentation on formatting a date in JavaScript? for more details on formatting dates.