1
general::
1. Seriously involved; far advanced. For example, He was in deep with the other merchants and couldn't strike out on his own, or She used her credit cards for everything, and before long she was in deep. 2. in deep water. Also, in over one's head. In trouble, with more difficulties than one can manage, as in The business was in deep water after the president resigned, or I'm afraid Bill got in over his head. These metaphoric expressions transfer the difficulties of being submerged to other problems. The first appears in Miles Coverdale's 1535 translation of the Book of Psalms (68:13): "I am come into deep waters." The second, which Also can signify being involved with more than one can understand, dates from the 1600s. Also see OVER ONE'S HEAD.
American Heritage Idioms
2
general::
Phrase(s): in deep
1. Fig. deeply involved (with someone or something). • Mary and Sam are in deep. • Wilbur got in deep with the mob. 2. Fig. deeply in debt. (Often with with or to.) • Willie is in deep with his bookie. • I’m in deep to the department store.
McGrawhill's American Idioms And Phrasal Verbs