1
general::
Overpower, overcome; also, get through the hardest part of. For example, This new offense has broken the back of the opposing team, or We're well over halfway there; we've broken the back of this journey. [Mid-1800s]
American Heritage Idioms
2
general::
Phrase(s): break the back of something
Fig. to end the domination of something; to reduce the power of something. • The government has worked for years to break the back of organized crime. • This new medicine should break the back of the epidemic.
McGrawhill's American Idioms And Phrasal Verbs