New Mexico Blue Hole... I'm wondering if we're thinking of the same thing... a very, very, very, very, very long time ago my family traveled the western USA. I was about 7. I can still remember visiting a circular pool of water in solid rock. This was not like a 'blue hole' you describe, however.... more like a cylindric hole in solid rock, somewhat small, and filled with water. The guide told us that the bottom had never been discovered. That fascinated me, and stuck with me, to this day. Of course... I'm not even sure this was in NM... too long ago.
Now that I think about I've heard of, seen a few times, many things called 'bottomless pits'. One of the caves in Calif., either Moaning or Mercer, is, (or was), said to be bottomless... that is, the lowest depths had not been explored.