Elizabeth is a character who finds herself in a very difficult situation in life. It is clear from the text that she feels she is superior to those around her, yet by marrying her husband she has doomed herself to a working class existence and the death of her dreams. She is presented in the story as a strong woman who is proud, and who bitterly objects to her husband's drinking habits. The quote above that you have highlighted shows the way in which she thinks of her husband, as she anticipates the only way her husband will return to her house is when he is so drunk that other men have to carry him.
This quote therefore is important in capturing the sense of disappointment that Elizabeth feels about her life and her marriage. She sees her husband as working against her as she tries desperately to make a respectable home and to separate herself from other people in the community.
However, what the quote you have highlighted does not reveal is the romanticism that Elizabeth has or had, which led her to contemplate marriage to her husband in the first place. It is only at the end of the story, when she contemplates the corpse of her husband, that she is forced to accept that the failure of her life and marriage is largely a result of her own inability to truly understand and know her husband.