Perhaps - as J suggests above - the writer was simply taking the idiom one stage further...ie from sheets to towels, the latter being thicker and even more prone to getting soaked!
In a speech I recently heard, the speaker was talking about how impatient we all are nowadays. He referred to himself as sitting at his computer waiting for Google to come up with a response and shouting, "Come on! I haven't got all minute!"
Normally, of course, we'd say "I haven't got all day!"...but using 'minute' just makes the point about impatience more effectively. Same perhaps with sheet/towel, though I must say myself that - if this was his intention - it's a bit laboured and totally lacking the wit in the day/minute example.