up to neck

*up to one's neck (in something)

 and *up to one's ears (in something); *up to one's eyeballs (in something)
having a lot of something; Fig. very much involved in something; immersed in something. (*Typically: be ~; get ~.) I can't come to the meeting. I'm up to my neck in these reports. Mary is up to her ears in her work. I am up to my eyeballs in things to do! I can't do any more!
See also: neck, up
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.

up to (one's) neck

Deeply involved or occupied fully: I'm up to my neck in paperwork.
See also: neck, up
American Heritage® Dictionary of the English Language, Fifth Edition.
See also:
  • be replaced by (someone or something)
  • be replaced with (someone or something)
  • be remembered as (something)
  • be remembered as/for something
  • a ball and chain
  • ball and chain
  • at (one's) doorstep
  • at doorstep
  • at somebody's expense
  • at someone's expense