I started off by shutting down the power, and unbolting the control panel so that I could get to the pump. I then unbolted the electric motor from the base, and from the pump itself (A Hot Tub pump has two parts - the "Wet End", which is where the water circulates, and the impeller spins, and the actual electric motor itself), hoping that I would be able to remove the motor without actually removing the "Wet End". No such luck though, the impeller is tightly attached to the motor shaft, probably an "interference fit" (i.e. it is pressed on). So, there was nothing for it but to drain the whole hot tub, and remove the entire pump unit.
Getting the pump to the bench, the first thing I tried was manually turning the motor - there is a covered slot in the end of the shaft opposite the pump, which can be turned manually with a screwdriver. But with crunching and grinding, I could only turn the shaft about a 1/4 turn - not a good sign.
A little more inspection showed a water stain underneath the impeller housing - it looks like the main seal (which seals the water inside the impeller housing) had a leak - very small, but enough to start to contaminate the main bearing of the motor. When turning the motor by hand, the main bearing was obviously the blocking point, and forcing it to turn started to release some rusty debris - looks like the main bearing had actually rusted and disintegrated!
Now fixing this is not beyond reason - but does require some specific tools for pulling and pushing bearings, and requires finding very specific repair parts. A little web research showed that I could purchase a brand new pump and motor for $260 (including shipping) - so I placed the order, and stuck the old motor on a shelf in the garage - fixing it will become a project for another time!
So, no hot-tubbing at the lounge for the time being, Which is a real pity as the new patio furniture and pirate-bar (complete with draft "Hop Along Silver" beer) is ready for christening!