Be rushed/run off your feet
Definition 1 of 1
Pro Tip 1/3Context of Busyness
Used when someone cannot spare time because they're occupied with too many tasks simultaneously. 
During the Christmas rush, the warehouse workers are run off their feet.
Pro Tip 2/3Informal Expression
Commonly used in casual or informal conversations rather than formal or business communication. 
I'd love to join you for lunch, but I've been rushed off my feet all morning.
Pro Tip 3/3Figurative Speech
It's a metaphorical phrase; there's no actual running or losing of feet involved. 
The caterers will be run off their feet at the wedding with so many guests.