I don't know if there is such a thing as groundhog grits, but I might be willing to find out just for spite.
I saw the big, fat, no-good whistlepig varmint today sneaking about my garden. Since I'm on injured reserve I couldn't chase the rodent. I've never been a redneck, never lived in a trailer, I'm not from the South but I don't quite qualify as a Yankee -- but I will spear the critter with my pitchfork given the chance. It's up to God and St. Francis to spare him if they want him.
In the meantime, the Frugal Yankee has a boatload of woodchuck/groundhog/whistlepig recipes.