What does "Go and put the monkey on his back" mean?. Is it a general American expression?. The men do not have an animal with them so the monkey is meaning something else yes?.
I can explain context if this is important.
It sounds to me like it's a play on "get the monkey off one's back", a fanciful term that's usually used (I think) for overcoming an addiction such as drugs or alcohol, although I think it can be used to refer to getting rid of some other kind of burden as well. We usually don't speak of having a monkey on one's back, only getting it off. So to "put the monkey on his back" sounds like a humorous way of inverting the expression, so it means something like giving alcohol to an alcoholic, or whatever fits the situation: basically adding rather than removing the burden in question.