The cable has to be long enough to reduce the Coriolis effect, and strong enough to support the "weight"
The non-rotating center of mass between the two could contain navigation and communication equipment.
Here's a link to a 300K movie.
No way you'd want to have a non-rotating center -- that means all sorts of moving parts, bearings, seals, and so on.
Another major problem would be attitude control. How do you point the little guy when you need to do a burn?
Probably the biggest problem would be mass balancing. You'd have to be extremely careful about that, and it'd be very difficult to manage.