2000 Dodge Neon engine governor cutout

Sitting in park and depressing the accelerator pedal causes the engine to rev, then at high rev cut out. The engine continues to rev up, then spontaneously cut out, dropping the revs, then back up again, etc.

Recently, this problem has migrated to the driving side of the car. When I accelerate into hard overdrive, the engine will cut out at high revs just as the transaxle drops into overdrive. The result is no acceleration, a corresponding shift out of overdrive, and the whole cycle starts again, jerkily if I don't back right off of it.

What is causing the engine to cut out at high revs?