I find it interesting that some people can do these in seconds (I think I'm fast, though certainly not world class). Others have no hope, even though they admit familiarity with the phrase once revealed. Some of my dyslexic friends are in this category. For instance, puns seems to escape them completely. This ability (or lack) seems to involve connections across the language areas of the brain, and is a side effect of learning and understanding languages of any kind. And it seems to be independent of overall intelligence.
Similarly, there are people who can see those 3D stereograms very quickly, and others who never ever get it.