I believe the song was written by the country/western singer Carol Baker. Here is her performance of that song (from CBC): YouTube - Carol Baker. One Drinks One Too Many. And a Thousands Not Enough. 1978.avi

Other 'recovery' songs include "Hooked On A Feeling" and "Make My Life Shine". (I'm not into country music; I'm a counselor, specializing in substance abuse-crisis intervention.)