The appearance of an unseen voice, claimed by Thoreau to be Congressman Abraham Lincoln, shows the specific position of anti-war advocates. While Lincoln presided over a brutal Civil War, the sense is that Lincoln's war was fought out of necessity, while the Mexican-American War was fought out of deliberate greed. Lincoln represents the voice of reason, while Ralph Waldo Emerson -- representing President James Polk -- ignores all reason in favor of endless debate while the war wages on.
LINCOLN: ...This unnecessary war was unconstitutionally commenced by the President, who may be telling us the truth -- but he is not telling us the whole truth. He has swept the war on and on, in showers of blood. His mind, taxed beyond its powers, is running about like some tortured creature on a burning surface!
(Lawrence and Lee, The Night Thoreau Spent in Jail, Google Books)
For Thoreau, who is passively protesting the war by not paying taxes, this shows the intellectual dishonesty of Polk's arguments; Polk wanted to annex more land, and refused to listen to any considerations that the plan might be untenable or immoral. The presence of Lincoln also showcases the difference between necessary and unnecessary war; Lincoln had no choice in the matter of Civil War, but was pushed into it by events beyond his control. Polk, in contrast, pushed the war as a way to claim more land for the United States, and so waged war almost for its own sake. This argument is also related to the years when the play was written and produced; many people believed that U.S. involvement in the Vietnam War was unnecessary, and that the war was being fought with dishonest intentions.