I strongly recommend having a 'drop dead' time for drop offs. That way you don't run into this issue AND your day is more scheduled (translation...not interrupted). My daughters daycare has a drop off by 9 policy...and no pick ups during nap time 1-3pm. I never have had a problem with this and so I would think most other parents would also not find it an issue.
Daycare Ladies! Free yourself from unreasonable parents! Unite! LOL