According to Frank Kidson, the famous Joey Grimaldi used to perform a version of Week's Work (1820-ish). The poet John Clare knew it, and later on several of the early 20th century collectors found forms of it in Southern England (see, for example, On Monday Morning) and of course it's been found often enough in America too; at the moment, though, I'm inclined to think that we're talking about two separate songs here (I buy still less Dick's suggestion in the DT that there might be a connection between Week's Work and The Wife Wrapped in Wether's Skin) but little is certain in this life.

It occurs to me that there is another broadside song on the same general topic that might bear looking at:  Woeful Marriage.