The correct answer to this open question is the following.
To what extent was any level of the government (national, state, or local) of 1786-87 able to carry out the functions for which government is established?
Well, the big issue in those years was that the Articles of Confederation -the first form of Constitution in the United States- left a weak central government that was very limited. It only could manage the post office and deal with the Native American Indian tribe's issues, among other minor things. The states remained sovereign and had more power. The states could collect money through taxation. And if the central government needed money, it had to ask for it from the states.
To what extent were the purpose(s) of government listed in the Preamble threatened by anarchy during this period?
The risk was major and the government realized this with the incidents of the Shay Rebellion in Massachusetts. The central government could not raise an army, and the Shay Rebellion was a tough lesson to learn.
That is why the delegates of the states participated in the Constitutional Convention of Philadelphia, Pennsylvania, during the summer of 1787, to create a new form of government based in a new Constitution.