What arguments might one use to counter Thoreau's objections to the idea of a standing government?
The histories of most countries include episodes many of their citizens might prefer to forget. In the United States, the practice of slavery and institutionalization of racism is an example of a government-inspired or actively supported policy that it could be argued would justify not just civil disobedience, but even violent resistance. In a certain time, and in a certain place, it is conceivable to imagine a political system in which such resistance is warranted. Anarchists believe in a society without government, and history has examples of anarchists using terrorism in opposition to the institutions of government.
Henry David Thoreau lived in a time when civil disobedience could be argued to have been warranted, particularly given the destruction that would soon ensue as the Civil War raged over the issues of states rights and slavery. That half of the country was ready to secede over the right for states to determine their own policies with regard to slavery would certainly influence the views of government of some people.
Whether the absence of a standing government is the answer, however, is highly questionable. Putting aside the natural expansion in the size of the federal government resulting from the policy of Manifest Destiny and population growth, history has determined that a standing govenment is essential for the maintenance of a civil society. Take, for instance, the role of law enforcement agencies in society. Ideally, there would be no need for police departments, at least on a permanent basis. Because people disagree, however, and because those disagreements frequently result in violence, the need for a police force is evident. Similarly, the fact that psychopaths exist -- as distinct from sociopaths -- means a mechanism has to exist to prevent or respond to acts of violence or other criminal acts they perpetrate.
That, however, is only one small facet of government, although ensuring public safety is one of the most important. The United States Government has grown due in no small part to the demand of the public it purports to serve. The American people expect a social welfare system to assist the less fortunate; that requires governmental institutions to raise funds and administer programs. The American public expects good roads on which to drive; that requires an organization to design, build and maintain those roads.
Absent a government, committees would be performed to carry out these responsibilities. Those committees are the basis of a government.
The Legislative Branch of government, for which this educator worked for 20 years, grew enormously just over the last 50 years, due entirely to the size of workload congressional offices began to encounter as populations grew and demanded assistance in all kinds of matters.
Similarly, the Judicial Branch of government -- and it should be pointed out that the highest court in the land, the U.S. Supreme Court, is in recess for several months out of the year -- is required to adjudicate differences of opinion and criminal matters on a regular basis.
Finally, the Executive Branch, with its many departments and agencies, including the armed forces, has proven to be needed on a year-round basis by virtue of the workload that comes with office. The Founding Fathers may have had different ideas about standing governments and armies, but they lived in a much smaller country in a far different time, and weren't able to pull it off themselves.