The significance of the Defarge staircase is that it symbolizes the poverty to into which the lower classes have been forced.
The staircase is described as a “gloomy tile-paved entry to the gloomy tile-paved staircase” and there is never anything positive about it. It is described as “vile” and common in the “older and more crowded parts of Paris” (1:5, p. 23). It represents a way of life that no one would choose if not forced into it.
When Lorry ascends the staircase, he is shocked and offended. There is garbage on every level.
The uncontrollable and hopeless mass of decomposition so engendered would have polluted the air, even if poverty and deprivation had not loaded it with their intangible impurities; the two bad sources combined made it almost insupportable. (Book 1, Ch 5, p. 23)
The staircase is a metaphor for the conditions in which these people live. They are dejected and miserable. They live like animals. There is no light let into the staircase, and there is no light in their lives. Thus the staircase foreshadows revolution, because it gives us a glimpse of the people’s lives.
At this point in the story, the reader does not know the significance of the Degarges or their role in the revolution. Our first encounter with them might bring up feelings of pity, but it doesn't. It produces disgust and a sense of disease. These Defarges may be up to no good.