Although the phrase "sweep me off my feet" probably means, "make me fall in love with you in a short time", what does it exactly mean, because "sweeping" can be difficult to be associated with "love". (It can be difficult to read the words "sweeping" and "feet" to get a feeling that it means love).
Below is one of its usage in Steve Jobs's letter to his wife:
We didn’t know much about each other twenty years ago. We were guided by our intuition; you swept me off my feet. It was snowing when we got married at the Ahwahnee. Years passed, kids came, good times, hard times, but never bad times. Our love and respect has endured and grown. We’ve been through so much together and here we are right back where we started 20 years ago—older, wiser— with wrinkles on our faces and hearts. We now know many of life’s joys, sufferings, secrets and wonders and we’re still here together. My feet have never returned to the ground. -- Steve Jobs