put (one's) back into (something)
To put a lot of effort into doing something as quickly or effectively as possible. Come on, we need to get this car off the road. Put your back into it and push! It's clear that the legislators have put their backs into crafting a bill that will find support across party lines, as well as in the general population.
put one's back into it
Make a strenuous effort, as in If you put your back into that report, you'll soon be done. This idiom alludes to physical labor involving the strength of one's back. It was first recorded in 1882.