This may seem to support the “length of the ammunition belt”, But this explanation, while tempting, doesn’t work. Here are the main reasons, from the article linked below (which nicely explains what we know–and esp what we DON’T know– about this expression). Note esp. the FIRST reason.

“First, ammunition is never measured in length of the belt. It is measured in number or rounds or in weight.

“Second, the phrase is absent from WWII literature. If it were of WWII vintage, citations of usage dating back to the 1940s would certainly have been found by now.

“Finally, the explanation itself doesn’t appear until the 1990s. . . ”

http://www.wordorigins.org/index.php/more/573/

The link includes this and other possible explanations.