What is the origin of the code-phrase, "The fat man walks alone"?

This phrase is used generically as a more or less "standard" espionage
code or password.  It appears in numerous film and television
references, with notable examples including the 1995 film "Empire
Records", 1992's "Mo' Money", and an 80's episode of "Family Ties"
guest-starring Tom Hanks.  It shows up in a well circulated joke list
of "101 things to do while shopping" [variously at Walmart, K-Mart,
etc.].  In all cases it's clearly meant to be recognized as a
well-known reference to code phrases (often paired with Neil
Armstrong's "The Eagle Has Landed"), but I've never found the original
source.

I've suspected but never confirmed that it may be related to the U.S.
mission dropping the atomic bomb known as "Fat Man" on Nagasaki.

If you do a search on google groups on the code phrase, one of the
messages states that it is from the manhatten project.

Unfortunately the original poster of that Usenet message was just
guessing.  The posting is from nine years ago--and was originally
addressed to me.

Dear mephigonz,

I am quite sure the quote comes from the thriller novel 'The Eagle has
landed' by Jack Higgins where in 1943, a detachment of German
Fallschirmjägers disguised as Polish exile paratroopers in England
have the order to kill Winston Churchill. As far as I remember, 'The
Fat Man walks alone' was the code for 'Churchill (= the Fat Man) is in
his summer residence, nearly unguarded'. Unfortunately, I can not
prove it.

Regards,
Scriptor