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.)