The very first thing you check is both u-joints. Get underneath the car and grap one yoke with one hand and the other yoke with the other hand and see if there is any looseness between them. Also check that the c clamp nuts that hold the rear u-joint caps into the pinion yoke are tight. Checking the u-joints is not something that you can do by just looking at the drive shaft. A vibration in the seat of your pants, especially one that just started, is 95% of the time u-joints. If this doesn't help get all 4 tires balanced and while the rear tires are off check that the brake drum weights haven't flown off.
Terry