Tough question to answer generally. In my residency program, we ranked candidates after their interviews on the same day. These were relatively fluid until the last group of candidates interviewed. On that day, all candidates were ranked and put on our list for the match. It literally took an act of God (i.e. the Chairman) to change that rank list once we decided the overall one on that last day.
Therefore, the best advice I can give you is to have that call made before the last group of candidates interview. If you interview on their last day, I would probably recommend your "doc" call theirs prior to the interview, but this is less than ideal.
Overall it would be best for them to call a day or so after you interview because you'd still be reasonably fresh in the minds of your interviewers. In other programs, they may not rank on the same day as interviews--this works in your favor if you have someone making a call on your behalf. In some programs, only the chairman or their trusted right-hand man can make changes after each rank is put down, so a call may not be as effective unless it's to one of these people. It really all depends.
Also, keep in mind that these calls are not the norm. Someone really has to go to bat for you and really like you to do it because they're putting their rep on the line for you. You'd better be worth it. Also, if you have 15 people applying from your med school class, I guarantee your chairman isn't willing to make calls for all 15--even they're even willing to do it, it'll only be for one probably. Don't ask an attending to do this lightly, all you will do is piss them off unless you have a good relationship with them. For a student, that's not real common.