This idiom or expression has to do with:

Surviving.
Trying to stay in business.
Trying not to fail in difficult times.
Saving, or trying to save, oneself.
Saving, or trying to save, one’s business.

Q. Do you want to join us on our trip? You need a vacation from work, you know.
A. I’d love to, but I have to work. I’m barely keeping my head above water as it is!