From the first moment the reader is aware of her, Madame Defarge is associated with her knitting needles. Traditionally, knitting needles evoke feminine domesticity, but Dickens links Madame Defarge's knitting with the ancient Greek concept of the Fates. The Fates are in charge of thread that measures out the lifespan of mortals. When this thread representing a human life is cut, the person associated with it dies. In general, they are usually presented as old women.
Madame Defarge's presence is as grim as any of the Fates, and her knitting needles hide a more sinister purpose. She is secretly creating a registry of the enemies of the coming revolution. In general, her presence is foreboding rather than warm or maternal. She exudes a sense of quiet determination and purpose.
Madame Defarge's link with the Fates is especially emphasized when the Marquis runs over a peasant child. When his attempts to pay away the damage (which are useless considering that the child is dead) are rebuffed, he condemns the assembled crowd as "dogs," and all of the peasants keep their eyes down—save for Madame Defarge, who is self-possessed enough to keep staring:
So cowed was their condition, and so long and hard their experience of what such a man could do to them, within the law and beyond it, that not a voice, or a hand, or even an eye was raised. Among the men, not one. But the woman who stood knitting looked up steadily, and looked the Marquis in the face. It was not for his dignity to notice it; his contemptuous eyes passed over her, and over all the other rats; and he leaned back in his seat again, and gave the word "Go on!"
This contrast from the rest of her fellow peasants gives Madame Defarge an almost supernatural feeling. Even as the crowd disperses, Dickens describes Madame Defarge as "still [knitting] on with the steadfastness of Fate." Later on in the story, Madame Defarge will use the names knitted into her registry as a way of identifying and then killing undesirables during the revolution. Like the Fates of old, she is literally deciding who lives and who dies.