Why do people say "Work like a dog?"

To mean working hard?

Dogs just lie around and nap. That's not working hard...

Solution 1:

"Sheepdogs" are definitely a reason. This link here, also offers another explanation:

In olden days, the two sawyers who worked on a tree sawing planks were the top-dog and the under-dog. A dog in those days was a manual worker. (Emphasis mine)

Perhaps the expression could also have come from a comparison with a "manual worker".

Solution 2:

I believe the term comes from herding dogs. I'm not a farmer, but from what I hear they work their little canine tails off to help with the herding.