Possibly from the proverb, recorded by Thomas Fuller in his Gnomologia as "Tis the last feather that breaks the horse's back." This comes from an Arab proverb about loading up a camel beyond its capacity to move, to the scenario of a single straw of grass or hay overwhelming the desert-roaming beast of burden.
the straw that broke the camel’s back
- (idiomatic) A small and seemingly insignificant addition to a burden that renders it too much to bear; the small thing which causes failure, or causes inability or unwillingness to endure any more of something.
- 1848. Charles Dickens, Dombey and Son:
- As the last straw breaks the laden camel's back.
Derived terms 
The small additional burden which causes failure