I don't remember where I heard it but "It is OK to disappoint but not OK to surprise" rings so true. Also, the earlier you know you'll be late the bigger the chance is that additional help can avoid the late delivery.
That's my experience too: as long as you keep people up to date and your updates follow some sort of schedule, late delivery is generally tolerated, especially when it can be seen coming from a reasonably long way off.
I always try to front-load the riskiest and most difficult work on projects for this reason: that way you're never in the situation where everything looks fine until it all goes off the rails at the last minute.
As long as one is careful to head off the "here are 10 entirely new people to help you make up the time" trap (with credit to Mythical Man Month of course).
I've never heard that saying btw but it's a great one, I'll definitely remember it for future use!
I always try to front-load the riskiest and most difficult work on projects for this reason: that way you're never in the situation where everything looks fine until it all goes off the rails at the last minute.