I have a Whirlpool washing machine, and am pretty sure I need to replace the motor coupler. I got the cabinet off; unclipped the pump (removed the hoses -- oops, probably didn't have to do that); and it LOOKS like the pump could be coaxed off the motor -- and it almost does. The bolt-like drive (?) coming out of the motor looks a bit rusty -- could that be the problem? Do I take off the motor WITH the pump still attached?

Any help greatly appreciated!

The rusted motor shaft is the problem. You can take the motor out with the pump still attached to replace the coupler, but you still have the leaking pump. I have had some luck getting the pump off, but sometimes its stuck so badly and I tried so hard to get it off (including busting the pump into many pieces) that the motor bearings get screwed up. If you are able to get the pump off, clean the motor shaft with some sandpaper or wire brush to remove the rust. If you do a good enough job, the new pump will just slide right on. Good luck.