To get in trouble, or into an embarrassing situation. Presumably the allusion here is to water hot enough to burn one. Although Lord Malmesbury wrote in a letter in 1765, “We are kept, to use the modern phrase, in hot water,” the term had appeared in print more than two centuries earlier. In the sixteenth and seventeenth centuries it was put as “to cost hot water.” It was probably already a cliché by the time it appeared in Richard H. Dana’s Two Years Before the Mast (1840): “He was always getting into hot water.”