put (one's) back to (something)
To put a great deal of effort into some action or activity. Come on, we need to get this car off the road. Put your back to it and push! It's clear that the legislators have put their backs to crafting a bill that will find support across party lines, as well as in the general population.
put one's back (in)to something
1. Fig. to apply great physical effort to lift or move something. All right, you guys. Put your backs into moving this piano. You can lift it if you put your back to it.
2. Fig. to apply a lot of mental or creative effort to doing something. (From {1}.) If we put our backs to it, we can bake twelve dozen cookies today. The artist put his back into finishing the picture on time.