I haven't watched such a manoeuvre being performed (only the parody in Spaceballs), but it is conceivable that direct pressure on or near the carotid sinus could trigger a baroreceptor reflex (mediated by nerves connecting stretch receptors in said sinus, the brainstem, and the heart and blood vessels), resulting in a precipitous fall in blood pressure, and syncope (fainting). (In fact the procedure has some diagnostic and therapeutic use for patients in hospital, where it is known as carotid sinus massage.)
- Sherwood, L. Human Physiology; West: Minneapolis, 2nd ed.; 1993, 334.