1. extremely busy, deeply involved in something
I'm up to my eyes/neck in work/debt/problems
If you are ‘up to your eyes’ it means you are extremely busy and have a lot to do. This expression is also used to highlight the extremity of a situation or to exaggerate. Similarly when you are ‘up to your neck’ it means you are deeply involved in something, extremely busy, or immersed in something. You can use both of these expressions to talk about dealing with a big problem. These are casual idiomatic expression but you can hear them used in both social and professional contexts. Similar in meaning to ‘in over my head’ and ‘to be run off your feet’.