To be swamped (with debts, work, responsibilities, and so forth). The analogy in this expression is to being in water over one’s head when one presumably is not a good swimmer. In the early seventeenth century it was put simply as over one’s head, as in “That silly women shall be dipt over head in a Gumble-stool for scolding” (Richard Baxter describing a ducking-stool in 1653).