sweep or carry or knock off someone's feet. Overwhelm someone emotionally; infatuate someone; make a very favorable impression on someone. For example, Winning first prize knocked her off her feet, or With his little gifts and gallant behavior, he swept her off her feet, or That fine speech carried him off his feet. The term using sweep dates from about 1900, carry from the mid-1800s, and knock from the early 1900s.
run or rush someone off his or her feet. Work someone to the point of exhaustion, hurry or pressure someone, as in With all the preparations, they've been running me off my feet, or The waiters were rushed off their feet. These hyperbolic expressions allude to running or hurrying so much that one falls down. The first dates from the mid-1800s; the second was first recorded as rushed off one's legs in 1916.