Literally 'wrap it on my body' - the image is of strapping responsibility onto yourself. The strongest 'leave it to me' in common Chinese: full guarantee, chest-thumping confidence. Slightly old-school / heroic flavor, often used half-jokingly among friends.
memory
Picture literally wrapping 包 the problem onto your body 身上, if it falls, it's your fault. That's the commitment level 包在我身上 promises.
