Direct calque of the English 'hot potato'. Almost always a noun (modern set phrase rather than a verb-phrase chengyu) — 接过烫手山芋 (to take on...), 甩出烫手山芋 (to offload...), 成了烫手山芋 (to become...).
memory
Picture a freshly roasted 山芋 (sweet potato) too hot to hold — you want to toss it to someone else as fast as possible. That's exactly how a problem nobody wants feels.
