Try
julianDate[date_DateObject] :=
 Module[{julian0},
  julian0 = 
   CalendarConvert[
    DateObject[{-4713, 1, 1, 1}, TimeZone -> 0, 
     CalendarType -> "Julian"], "Gregorian"];
  DateDifference[julian0, date]
  ]
then 
julianDate[DateObject[{2014, 10, 16, 14, 10, 04}]]
gives
Quantity[2.456947715324074`*^6, "Days"] 
Note that I am using midnight as the reference time for the julian zero date.  This URL says that it should be noon:  http://aa.usno.navy.mil/data/docs/JulianDate.php  but I set it to midnight to conform to your calculation, and the statement on that site is probably in error: midnight makes the most sense, of course.
(I fixed a small typo in the code of an earlier version of this post.)