Meaning: ridiculously busy
Rewrite 1: busier than a one-handed paper hanger
Rewrite 2: busier than a dog-walker in a yard full of cats
Rewrite 3: busier than a pumpkin-carver on a steep hill
Rewrite 4: more distracted than a cross-dresser in a locker room

Comment: There are a lot of interesting prospects for this cliché. Obviously the more extreme the case the more fun the metaphor. The last one above is a bit weaker than the others, but it still serves as an example of someone busy in very different, if not extremely different, circumstances.