If you have the older style vertical motor with impeller and it will not come off, here is a procedure for this.
First thing, trying to torque the 1/4 inch screw off with a nut driver and vice grips is a bad idea, might just bust the screw off in the motor shaft.
Take a sharp wood chisel and gently pound down on the top edge of the impeller close to the screw. Crack it away from the shaft, then put penetrating oil on the screw and take it off. Works every time, just be careful not to pound down too hard, might damage the motor.

richappy,

Saw your impeller removal advice but wish to remove the 1/4 screw, then replace after cleaning an obstruction. For that reason, I don't want to crack the rubber washer. I've had a specialized nut busting solution on it for three days now so perhaps that will help. Do you know if the screw is REVERSE THREADED? Is it removed by turning clockwise?

Thanks!

Is there really no way to remove the impeller without destroying it?

I'm trying to remove the impeller so I can get to the screws under it that hold the filter in place, it's horribly clogged with hard-water build-up.

You where lucky, it was not seized, most of them are. Sometimes, if you twist it back and for a few times it will come off without breaking off. It shows some ability on your part to sense that it will not break off, good job.

You got the wrong dishwasher shown on ref. parts at Sears. Re-post your model # in the box so we can easily look it up.