If (one's) life depended on it phrase
This phrase is generally always used in combination with a negative statement about something you couldn't or would't do.
No matter what.
I wouldn't help her if my life depended on it. As I have told you before, she is a cruel girl.
I couldn't win your heart if my life depended on it. It's time for me to give up.
They wouldn't agree to split up the company if their life depended on it.