Your understanding of our system is imperfect. The executive authority in our systems rests in the Executive Council, the Governor-General(representative of the crown of Australia not Britain) acting upon the advice of Ministers of the Crown. Each of those Ministers of the Crown are elected representatives, not appointed officials, who must answer to the parliament as a whole, and only to select committees on a few specific occasions where the parliament delegates its authority. For practical day to day operations, the Prime Minister oversees the process and the Ministers in caucus agree the course of action
A good example of how it works is that a Royal Commission has just been instigated to examine child abuse in various institutions and will be wide ranging enough to enquire into police handling of cases. No Parliamentary Select Committee could investigate in sufficient detail. Parliament has delegated its authority to a judicial process. This has gotten beyond a state process because bodies have acted across state borders to usurp the course of justice
In 1975 the monarch of Australia sacked the PM and the government of the day because they no longer had the confidence of the people and could not guarantee supply, the equivalent of your fiscal cliff. This forced an immediate election at which the people upheld the action taken. Your ideas of what we might accept or not accept are way off

