To attract support is a problem (8)
I believe the answer is:
drawback
'problem' is the definition.
(thesaurus)
'to attract support' is the wordplay.
'to attract' becomes 'draw' ('draw' can be a synonym of 'attract'**).
'support' becomes 'back' (back is a kind of support).
'draw'+'back'='DRAWBACK'
'is a' acts as a link.
(Other definitions for drawback that I've seen before include "Snag" , "Hindrance - retreat" , "Obstacle" , "Hindrance - disadvantage" , "Fly in the ointment" .)