The most common and most likely answer to this crossword clue is the 2 letter word UH
I've seen this crossword clue in The Times
U
H
Buddy explains!

The straight part
We know that "Negative response" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case negative response = uh.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does UH mean?
UH noun- An occurrence of the interjection "uh".
- Expression of thought, confusion, or uncertainty.
- Space filler or pause during conversation.