Yeah, Date object complects date and time, so comparing it with just date value does not work.
You can simply use the $where operator to express more complex condition with Javascript boolean expression :)
db.posts.find({ '$where': 'this.created_on.toJSON().slice(0, 10) == "2012-07-14"' })
created_on
is the datetime field and 2012-07-14
is the specified date.
Date should be exactly in YYYY-MM-DD format.
Note: Use $where
sparingly, it has performance implications.