Support group? Most of family quite failing to get it (6)
I believe the answer is:
claque
'support group?' is the definition.
(claque can mean a group of followers)
I don't understand the remainder of the clue.
(Other definitions for claque that I've seen before include "Group of hired applauders" , "Hired-applause team" , "Supporters" , "Group of followers hired to applaud at a performance" , "Group hired to applaud someone" .)