If someone suffered because of you, you are responsible. Even if “they could have made a better choice”.
If someone is following up with you but you are unable to do the thing, it makes practical sense to buy some time. Leaving someone hanging even though they are much better off than you never solves the problem.
If you think you can do a task by tomorrow, take time for two days. Just in case the task doesn’t get done, at least you have a buffer.
Accountability is a wise man’s armour to relationships and reliability. People too busy to look beyond themselves cannot usually afford it.