We had this mad, self-destructive urge (5,4)
I believe the answer is:
death wish
'self-destructive urge' is the definition.
(thesaurus)
'we had this mad' is the wordplay.
'mad' is an anagram indicator.
'we'+'had'+'this'='wehadthis'
'wehadthis' is an anagram of 'DEATH WISH'.
(Other definitions for death wish that I've seen before include "Desire to pass on" , "Unconscious desire to end it all" , "Desire for self-annihilation" , "destructive feeling" , "Reason for very reckless acts?" .)