Given the many suggestions that the line was likely frozen inside the freezer door, I wanted to let the door warm up. I moved the contents of the freezer door shelves into the freezer and then taped a large piece of flat cardboard over the entire freezer box. I taped the door switch so it stayed depressed (so the freezer thought the door was closed and thus the fans started up and the water dispenser could be tested). I left to door open a while (maybe 30 min) and the water dispenser again worked. Others have indicated the typical spot of freezing is in the door just below the ice shoot (@AppGuy provided this diagram). I suspect my problem was too much stuff in the freezer box on the shelf adjacent to this spot on the door.