Sigh with a debate rambling: an expression of annoyance (5,3,3,4)
I believe the answer is:
whats the big idea
'an expression of annoyance' is the definition.
(phrase said when annoyed with a situation)
'sigh with a debate rambling' is the wordplay.
'rambling' indicates an anagram.
'sigh'+'with'+'a'+'debate'='sighwithadebate'
'sighwithadebate' with letters rearranged gives 'WHAT'S THE BIG IDEA?'.
(Other definitions for whats the big idea that I've seen before include "Affronted comment" , "highlighting philosophical notion?" , "Question from advertising agency possibly" , "expression of incredulity" .)