Thoreau seems to believe that slavery will never be eradicated through the democratic process, at least not in the foreseeable future:
There is but little virtue in the action of masses of men. When the majority shall at length vote for the abolition of slavery, it will be because they are indifferent to slavery, or because there is but little slavery left to be abolished by their vote.
This is part of his larger argument in "Civil Disobedience," namely that when the government and law stand behind an unjust policy or an institution, as he viewed the Mexican War and slavery to be, that the only just thing to do was to defy government by refusing to support it. In his case, Thoreau chose to refuse to pay his taxes. But the idea was that a popular majority did not necessarily constitute the right, and the continued existence of, and support for, slavery was a particularly conspicuous example of this.
Additionally: Thoreau was dismayed and frustrated by the inability of the antislavery movement of his day to engender and enforce policy. In paragraph 10, he writes: “There are thousands who are in opinion opposed to slavery and to the war, who yet in effect do nothing to put an end to them.” Signing petitions, writing editorials, and holding meetings did not stop the practice. (His mother, aunts, and two sisters were heavily involved in such activities.) What was needed was some kind of physical action. He felt as if he had taken a small step himself by refusing to pay the state poll tax and by being allowed to be locked up in jail as a result. Perhaps by witnessing his example—and later, by listening to his lectures, or by reading his published essay, “Resistance to Civil Government”—other individuals would be moved toward some sort of action as well. In paragraph 20, he further explores the possibility of a ripple effect:
I know this well, that if one thousand, if one hundred, if ten men whom I could name – if ten honest men only – ay, if one HONEST man, in this State of Massachusetts, ceasing to hold slaves, were actually to withdraw from this copartnership, and be locked up in the county jail therefore, it would be the abolition of slavery in America. For it matters not how small the beginning may seem to be: what is once well done is done forever.
Unfortunately, Thoreau did not live to hear President Lincoln issue the Emancipation Proclamation in 1863. One wonders if he would have thought the document went far enough.