Civil liberties in the forever war
First of all, even from Lincoln the question was rhetorical and the rhetoric was exaggerated. Even had the North lost the Civil War, some very desirable laws would have taken a beating (e.g. laws that ended up being promulgated to ban slavery in the South), but the execution of most other laws would have gone ahead as before. Furthermore, most of the cases being adjudicated typically occurred well away from enemy lines and in late stages of the war when there was no serious danger of the South winning.
Nevertheless, Abraham Lincoln faced a far more difficult problem with the execution of the laws than governments fighting the "War on Terror" face today. When Lincoln made this quote it was plausible; applying it to today's situation is not. Despite the difficulties the Union faced, its judiciary endeavored to preserve the rights of civilians against military encroachment. One very good result of that, which should be closely heeded by Courts today, is Ex Parte Milligan. Despite a Civil War far more damaging to the normal execution of the laws than any imminent threat the United States has ever faced since, the Court held for liberty in wartime against the encroachment of authoritarian military justice.
Civil liberties take their greatest hits during wartime. First Amendment rights were violated in the United States after the French Revolution when the States were threatened by further rebellion and being drawn into the ensuing war between England and France. They were again trampled upon during World War I. The Holocaust in Germany and Korematsu in the United States occurred during World War II. Vigilance in protecting our liberties is at no time more important than during a perceived or actual "war."
Many argue that today we are again at war: the "War on Terror." If the Soviet Union had attacked the United States on 9/11, we would have gone to war with them, so the argument goes. Actually, the Soviet Union did attack the passenger airplane of a close ally, South Korea, killing several hundred people including many United States citizens and a United States Congressman. There was no serious argument at the time that this was an act of war. An act of war occurs not merely from an attack, but from an attack that seriously damages our military and threatens our territory, for example the Japanese attack on Pearl Harbor. That attack was no isolated attack for the sake of killing people and making headlines, but a very serious and, at least initially, very successful attempt to destroy American naval might and capture large pieces of its territory (e.g. the Philippines) and territory of its allies (French Indochina, Dutch Indonesia, etc.) Al Quaeda is full of some very sick people and stirs up quit a bit of torrid television coverage, but it is not a threat comparable to Imperial Japan.
Unlike earlier wars fought between governments to a conclusion, a "War on Terror" will last forever. It's like fighting a "War on Blitzkrieg" or a "War On Drugs" or a "War on Murder." Terrorism is a particularly evil type of violence that has plagued humankind since the dawn of history, and there is no sign that the evils of terrorism will be eliminated any time soon.
Professor Burt Neuborne of New York University School of Law compares the authoritarian military justice system with our civilian justice system. Some societies, such as China, have a justice system runs as if the society was in a permanent state of war -- as indeed might characterize the antagonistic relationship between Party members and the rest of society there. In the United States the justice system is bifurcated, with the authoritarian military justice system reserved for military personnel or enemies in war.
Neuborne observes that the authoritarian system that typically takes over governments during wartime makes three large errors in the pursuit of security that impact liberty: it overstates risks, it generates many false positives (i.e. persecutes people thought to be risky but actually innocent), and it is overly harsh. The current abuse of Lincoln's quote is an extreme example of overstating the risks. The Jews killed by Germany and the Japanese interned by the United States are extreme examples of false positives, and, at least of the former, of overly harsh reactions.
We must thus confront the question: are we to compromise our constitutional liberties and natural rights for the sake of a "war" of a very different kind and degree faced in Ex Parte Milligan? Assuming we are indeed at war, with an enemy that wears no uniform and may include American residents and American citizens, who gets to decide who is an "enemy combatant,” to be herded into the authoritarian military justice system, and who is just another alleged criminal with full constitutional rights? Those among us who long for more authority and destruction of liberty on the model of China, Nazi Germany, the Soviet Union, or some aspects of the United States itself during World War II, or who negligently ignore these nasty lessons of history, let their pining for security overcome them and argue that we can trust the authoritarian military justice system. In a free society it is the civilian courts, or at least courts with procedural protections comparable to the civilian courts, that ought to make that initial determination. In a free society it is the civilian courts under the fully unfurled umbrella of a constitution which should thereafter handle people who are not enemy combatants of a war power that threatens the very execution of our laws, but are just particularly evil and destructive criminals.