Generally speaking, no.
Service animals can generally accompany their disabled handler in the cabin of an aircraft with few exceptions. Those exceptions may include some exotic species and large animals. If a service animal is excluded from the cabin for any reason, and the airline has facilities for transporting the animal in cargo, then they should offer to do so for free.
If the service animal is too large to fit in the handler's foot space, and the plane is full, then the person can be required to purchase a second seat to provide sufficient foot space for their service animal. If there are empty seats on the aircraft, ask to be placed next to an empty seat instead.