to have so much work that you have problems dealing with it all.

She wants me to take some time off but I'm snowed under with work at the moment. (often + with)

• chocolate box
• choke off
• choke off something
• choke up
• choke you up
• chop and change
• Chop chop!
• chosen few
• chunk of change
• churn out
• churn something out
• circle the wagons
• claim to fame
• clamp down on
• clamp down on something
• clam up
• clapped-out
• clarion call
• claw way
• claw way somewhere
• claw your way
• claw your way back from
• claw your way back from something
• claw your way somewhere
• clean bill of health