In a trailer for the movie "Black Hat", one person says
"The guy we're working with will drop the big hammer and not think twice about it"
Is this some sort of American slang, possibly for a nuclear weapon?
Doing a onelook search for "Big hammer" only gives Urban Dictionary, with a meaning that wouldn't make sense here.
Best Answer
According to The Random House Dictionary of American Slang (1997), the phrase "drop the hammer on" has been used as an idiom since at least 1978:
As nearly as I can tell, the inclusion of big in the OP's example does not indicate that "drop the big hammer" is a fundamentally different idiom from "drop the hammer" (in contrast to "drop the big one," for example, where "the big one" refers to a nuclear warhead); instead, I read the word big as a simple intensifier tacked onto the older and simpler phrase.
It is possible (and perhaps even likely) that "drop the hammer" evolved from "put the hammer down," a trucking term. Robert Chapman & Barbara Kipfer, Dictionary of American Slang, third edition (1995) has this entry for hammer down: