Indeed they could. Daffodil sap is not only a skin irritant, daffodil bulbs have often been mistaken for onions and made into a soup either disagreeing violently with its consumers or even killing them. John Robertson of The Poison Garden tells of several poisoning incidents. In 2009, at a primary school in Suffolk, pupils used onions grown in the school's own vegetable garden for a soup. Unfortunately, there was one daffodil bulb among the onions and nearly a dozen of the children vomited and had stomach cramps. They were brought to hospital in time, and all of them survived. A four-year-old girl on the German occupied and starved island of Jersey during WWII was less lucky. She died after sucking the sap from a daffodil stem.
The toxic cocktail of alkaloids (Haemanthamine, Galanthine, Crinine, Galanthamine, Pluviine, Narcidine, in total 0.15% of wet mass) in daffodils are severe skin irritants and cause inflammation of the digestive tract if ingested, resulting in vomiting, diarrhoea and colic. Galanthamine acts on the peripheral and central nervous system by inhibiting the action of acetlycholinesterase (AChE), an enzyme needed for proper nerve impulse transmission. Symptoms are heart arrhythmia, ataxia (loss of coordination of movements, staggering, numbness), tremor, cramps and tetanus-like convulsions, bradycardia (lowered heart rate), hypotonia (drop of blood pressure). Death can occur through paralysis of the heart.
Onset of effects several hours to a few days after application / ingestion.
Dog: 15 g of bulb. For isolated Galanthamine the toxic dose for mice is 19 mg per kg body weight.
In Greek mythology, the young man Narcissus fell in love with his own reflection in the water, lost all interest in life and died as a result. The story is the origin of the term narcissism, i.e. a fixation to oneself. The word narcotic also stems from narcissus, for the narcotic, numbing effects of daffodil sap.