A short piece of advice for anyone stuck in this kind of situation. This advice was given to me years ago and I've found it to be true.
A customer will nearly always accept a piece that is late, but will never accept a piece that is wrong or incomplete.
If you're in a situation where you don't have time to finish, contact the customer, apologize profusely, and COMMUNICATE that you have to take some time to make sure it's right.
One of the worst problems I've had with vendors has been an unwillingness to man-up and tell the truth. If something is late, they will pretend not to get emails, or they won't answer the phone, or they'll have someone lie and say that they're unavailable. I even had to chew out a dear friend who made a knife that I wanted for a neighbor. He was embarrassed and kept ducking me. I told him in the future just talk to me; give me a new estimated date. I may be unhappy, but I won't be angry.