It really depends on what relationship you had with the doctor and his indications.
One of my letters was from a doctor I only shadowed for about 3-4 hours a day for 3 weeks or so. However, he was an anesthesiologist, so we spent most of the time discussing the case and talking about aspects of the medical field. After 2 days or so, the doctor began shaking my hand before and after I came and said "Nice working with you" when I left. He also offered to write a letter before I asked and said that I had made a good impression.
Obviously, a surgeon you stand behind (1 foot, avoid blue at all costs!!!) for infinity may acknowledge you but not have a chance to get to know you or observe how you react in a hospital setting.
My advice - pick an anesthesiology, internist, peds physician, etc. 🙂