From what I hear, if your medical is clean, it gets turned around promptly, but if there is anything to question, it will take weeks, if not months, and medical follow up that can take weeks or months.
I recently heard a story from a guy on a harbor boat that has to work days one week and nights the next week. He admitted on his physical form for renewal that he had been taking some over the counter sleeping pills to help him make the transition from days to nights. That delayed his renewal, required further medical exams, and put him out of work for a month when his license expired before the renewal.
I vaguely remember a story from another guy that took something like "Celebrex" (an expensive super tylnol type product) only to discover that it was on the secret USCG prohibited list. Apparently, a rare side effect is heart valve damage. He could not renew until he spent $5,000 for a CAT scan and had a cardiologist certify that he had no heart valve damage.
So take Nancy Reagan's advice: Just say no to drugs.