I drive a 6 speed manual and have the same problem. I have about 29k miles right now and have been complaining about this problem since about 3k miles. No one seemed to believe me until my boyfriend agreed with me. (Typical mechanics...)
I brought it into the dealership and they thought it was a bad throttle body and replaced the clutch and clutch housing. The noise didn't go away.
Brought it back a week later and this time they thought it was the engine mount, so they replaced that. Nope try again. The noise is still there.
I googled engine noise problems and came up with a forum thread about this exact problem. The person said a Nissan Field Engineer came out to look at the problem and found the bracket was not secured to the car and the steel Evap system lines were not installed correctly thereby causing the vibration.
Here's the link if anyone's interested in what else was said.
Nissan Versa Engine Questions - CarSpace Automotive Forums
One a separate note, I have two questions for you.
1. Does any one experience a (sometimes loud) high pitched whining noise coming from the engine, sometimes at low speeds but mainly during highway driving?
2. Have you noticed a clinking feeling and/or noise in the steering column when turning?
The dealership said they didn't find anything regarding my other 2 complaints. I really want to get it fixed soon as my warranty is almost up and with the miles I drive daily I could be out of warranty by the end of July.
Hope this helped you. Let me know if you have any other questions.
Cheers!!