I remember watching this on Discovery or some such channel recently:
5 25 "Boys Adrift" Survivors: Troy Driscoll and Josh Long February 19, 2010
In April 2005, Troy Driscoll and his friend Josh Long attempted to go shark fishing in a less than seaworthy boat. When a riptide drags them into the Atlantic ocean, they face extreme dehydration, hunger, and weather for 6 days while awaiting rescue, watching helplessly as other boats pass by without seeing them.
In the reconstruction they nearly went crazy. Hallucinating etc. One of the boys could not face being around all the sea water without being able to drink it in the end and drank some causing worse dehydration and vomiting. One of them I recall also picked up some kind of jellyfish type creature and ate it for relief. There were some real life pictures of them after the ordeal recovering and they were very badly sunburnt and thin I seem to remember.
So yeah...6 days is possible. Wouldn't advise it. You could die after just 2 or 3 days.