Is "Time is short and the water's risin'" a Southernism?

The only thing I found is this:

Time Is Short and the Water Rises, Operation Gwamba: The Story of the Rescue of 10,000 Animals from Certain Death in a South American Rain Forest. Hardcover – January, 1967

by John Walsh (Author), Robert Gannon (Author)

This seems too recent (1967) to be the source of a folk saying. However, the title could come from an older saying, which I have not been able to find so far.

A candidate for an older saying which your mother and her neighbors might have adapted is:

God willing and the creek don't rise

Sources: World Wide Words and Wikipedia, The creek don't rise

Note that the time is short is a Biblical saying (Paul, 1 Corinthians 7:29), which is extensively discussed at Biblical Hermeneutics Stack Exchange. It is thus possible that your mother's community combined a Biblical saying warning that time is short with an old regional saying about the rising [waters of the] creek (or crick). More Research is Needed.