I have been told by people close to adcoms that some schools will count a long turnaround for a secondary as a negative mark on an application. I don't know if Stanford does this however. If the school is telling you to get it done soon, I wouldn't recommend waiting anyway.
there are so many factors that go into a secondary turnaround, the least of which is lack of interest in the school (why would you apply if you didn't care?). For a school to hold it against you is pure conjecture, and they wouldn't do that because (a) it's unfair to applicants who had a legitimate reason for holding off for >2 weeks, and (b) they don't have the time/patience to try to figure out why we submitted so late. Just because we sit here and tried to read the minds of adcoms doesn't mean they do the same for us.