Who could actually grin while eating shit? I mean honestlly it has to taste just awful.
For what it's worth, here's the etymology of the phrase as it was explained to me in my youth:
The full, original phrase is "...like a possum with a shit-eating grin" (hereinafter abbreviated SEG). If you are familar with the opossum, you know that it's an omnivore that's noted for it's toothiness (
http://en.wikipedia.org/wiki/Opossum) Side note: I once worked with a guy who had a long nose and a big, toothy, but insincere smile. His behind the back nickname was the Opossum.
The conjunction of these two characteristics is that an opossum will eat feces and appear to be smiling while doing it. Hence the phrase SEG.