Also there are dozens of smaller things that should be checked before such a major repair. Sorry to rant but this just irked me.
GE washer designs of late have been noted for attempting to spin while in agitation. This causes water to overflow the tub and end up on the floor. You might be able to see if such is happening by opening the lid during the wash. BTW. It is normal to the wash tub to index (move an inch or two at a time) but not to do any full, uninterrupted rotations.
If this is the cause in your case, the transmission will either need to be serviced or replaced. If that is not the cause, opening the machine and looking for the point of origin will likely be necessary. A leak on a washer or dishwasher will often leave a trail of soap scum along it's path from the highest point.
The Appliance Information Site
[This message has been edited by DanO (edited February 12, 2004).]