Even though it's a common object, few pet owners know the potential hazards of the product. If the oil is used in your home, there is always the chance that your cat could be accidentally exposed. Most potpourri liquids contain natural or essential oils, which if ingested can cause vomiting, stomach upset, diarrhea, weakness, and possibly liver damage.
Some products also contain cationic detergents, in which case the signs tend to be much worse.
Cationic detergents can be caustic. This means that if ingested, it can actually burn the mouth and tongue. With eye or skin contact, there can be severe pain. If there is skin contact with the oils, the skin will become very red in color and be extremely painful to the animal. Instinctively, cats will tend to try to groom off the product, ingesting the potpourri.