I have a 03 monte LS , I notice a vibration while reaching 35 to 40 mph. And up. I had a bike rack on the trunk hauling three bikes and a full truck and while on the interstate it was very pronounced at times. Completely unloaded it isn't as noticeable. But is there around above mentioned speeds. Car is an auto and shifts fine.

 

You could have a wheel hub assembly starting to go bad, they are sealed units and contain the bearings.