Many Americans profess to be Christian and in the Christian and Jewish religion, suicide is a sin. Assisted-suicide is considered the same as suicide self inflicted.
If euthanasia would become legal doctors would be going against their oath and beliefs. Doctors' would have death on their hands by going through with euthanasia. Doctors would have to deal with pain of killing people by their own hand.
Doctors take an oath of protecting their patients when they graduate from medical school and it would go against everything they went into when going into medicine.