I've done that. Took us a week... about 2 and half days down and 2 and half days back up.
Started at Hite (which is dry right now), went to Halls Creek the first night, then the San Juan arm the second, and then down to Page on the third, messed around and then hauled ass back up to the San Juan. Didn't actually go all the way to the dam though. Camped at Hansen Creek on the way back up, and then back to Hite on the final day.
It was a long, fun, expensive week.