Down time

'Down time' is time when you don't have to be anywhere doing anything and can actually relax. It speaks to how over-programmed and over-scheduled so many Americans are.

Example:
-I really need some down time! I've been way too busy lately!
-Yeah, me too! (Sigh.)

All tied up

If you're 'all tied up,' it means you're too busy to do whatever the other person is asking you to do. It's a typical expression you hear in an office.

Example:
-Can you go to lunch next Thursday?
-No, sorry. I'll be all tied up in court next week. How about the week after that?

Knee deep in

'Knee deep in' is used to describe when someone is in the middle of doing something and doesn't want to or can't be interrupted. The visual it suggests is that the person is standing in something that is up to their knees, and they can't easily get out, if out at all. It can be used as an apology.

Example:
-I'm sorry I can't go to lunch with you! I'm knee-deep in paperwork!
-Maybe tomorrow!