As a general rule, being a Person of One’s Word is highly admirable and a sign of character and integrity. But in some very special cases, it might do more harm than good.
In the rare circumstance, it might actually be better to bite the bullet and admit you made a mistake, to confess you underestimated the workload or overestimated the time you had to commit, than to push through and meet the deadline with a rushed solution. Whoever you’re doing the work for right now might be annoyed (or disappointed or frustrated or angry) about a week’s delay, and they might have every right to feel that way.
But in many cases, once your work is out there for the world to see, it has to stand on its own. There’s no special tag hanging off the side saying “Wrote this in three days instead of twelve!”, or “Could’ve been a lot better if I’d had two more weeks!”. For many people, whatever that project is, that will be their first contact with you and your work. It might be worth it to slip the schedule to make sure you’re representing yourself well.
Of course, it only works if it’s truly a rare case. (And if you’re not, you know, ruining a wedding or a funeral.) If you’re regularly missing deadlines or under-delivering, you’re digging a mighty hole for yourself in the long run. But if you’ve done the work and established yourself as a Generally Reliable Sort, you’ve got some Character Credit built up that can give you an emergency cushion, should you ever need it.