last-minute vs not a minute too soon

last-minute

adj
  • Just before it is too late; in the nick of time. 

  • Done or occurring at the latest possible time before an event. 

not a minute too soon

adv
  • after an undesirable delay; undesirably late 

  • at the last possible moment; just in time 

How often have the words last-minute and not a minute too soon occurred in a corpus of books? (source: Google Ngram Viewer )