Replying to Admin:
The expression is said to derive from the trench warfare in World War I Europe. One will find repeatedly the expression "being up to their neck in muck and bullets" .
There is a kind of universal meaning here, and the next stage of being "up to your neck" is "to be in over your head". A gesture sometimes seen is to tap the underside of one's chin with the back of the hand and say something like, "I've had it up to here", which easily translates to "being up to your neck." and not being too happy about it, that is to say, "fed up" with something.
Replying to [Admin]:be up to your neck - be exceptionally busy or deeply involved in something.
Examples:
So will you get a holiday this year?
~ I doubt it. I've no spare cash and I'm up to my neck in debt.She said she knew nothing about the robbery, but I'm sure she's in it up to her neck.
be up to your neck in something
1. to be very busy. Right now I'm up to my neck in work.2. to be in a difficult or unpleasant situation. He's paid practically nothing and he's up to his neck in debt.