break your back

break (one's) back

To put forth a great deal of effort. I've been breaking my back trying to get a passing grade this semester, so failing by two measly points is incredibly frustrating. Don't break your back trying to please these people—they'll never appreciate it.
See also: back, break
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.

break your back

If you break your back to do something, you work extremely hard to try to do it. When you're breaking your back to make a business work, it's going to cut into your time with family. `I had been travelling all over the country, breaking my back just to get a job,' she says.
See also: back, break
Collins COBUILD Idioms Dictionary, 3rd ed. © HarperCollins Publishers 2012

break your ˈback doing something/to do something

work very hard to achieve something: I’ve been breaking my back to sell as many books as I can. ▶ ˈback-breaking adj. (of physical work) very hard and tiring
See also: back, break, something, to
Farlex Partner Idioms Dictionary © Farlex 2017
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References in classic literature ?
"If you keep the Grand Gallipoot waiting, he'll break your back," declared the messenger.
1st Corinthians 10, 13 THE weight of your cross may give you a stoop but it will not break your back.