Giant deficit accepted by fellow-American (8)
I believe the answer is:
colossus
'giant' is the definition.
('colossus' can be a synonym of 'giant')
'deficit accepted by fellow-american' is the wordplay.
'deficit' becomes 'loss' (I've seen this before).
'accepted by' means one lot of letters goes inside another.
'fellow' becomes 'co' (I've seen this in other clues**).
'american' becomes 'us'.
'co'+'us'='cous'
'loss' going into 'cous' is 'COLOSSUS'.
(Other definitions for colossus that I've seen before include "An immense statue - there was one at Rhodes" , "VIP" , "Gigantic statue that stood at the harbour entrance at Rhodes" , "An immense state as once at Rhodes (8)" , "Great thing" .)