Can be deadly. The size of the clot dictates how dangerous it is. Very very tiny emboli may not have much clinical consequence, unless it happens frequently. A large embolus that blocks large amounts of flow to the lung can cause symptoms including shortness of breath and even cardiac arrest. Unexpected shortness of breath should always be considered an emergency and evaluated by a doctor right away!
Goolge PE. Pe: pulmonary embolism is what you are looking for. It is a potentially catastrophic event when clots (usually from legs or pelvic veins) travel back to the heart and get pumped into your lung. It will compromise your circulation and more importantly reduce your ability to re-oxygenate your blood.