I'm having the exact same problem with my General Electric (GE) WCSR2090DAWW and after taking my washing machine apart I have some additional info. It is as if the motor does not have enough power to start the spin cycle. When the machine goes into spin cycle, the motor gives a big jolt but not enough to kick into a spin.
I disassembled the agitator and loosened the large nut that holds the tub to the drive shaft. This made the tub much easier to spin, and the motor was able to kick into the spin cycle. However, it caused a lot of knocking because I assume the contact between tub and and drive shaft was not constant.