Press demur generally seeing major cutbacks (4)
I believe the answer is:
urge
'press' is the definition.
(I know that press can be written as urge)
'demur generally seeing major cutbacks' is the wordplay.
'seeing major cutbacks' says the answer is hidden in the clue (lots of letters are cut from the word).
'URGE' is hidden within 'demur generally'.
(Other definitions for urge that I've seen before include "Compulsion; egg on" , "Sudden inclination to do something" , "Advise earnestly, spur" , "Advise strongly to press forward" , "Advise earnestly, prod" .)