Elephant

The phrase "out of the woods" is an idiom used to convey the idea of emerging from danger or hardship. In this case, Billy uses the idiom as a way of convincing the narrator that it won't be long before he'll be able to repay the borrowed money—he just needs to get financially "out of the woods," which he claims will only take two months. 

The use of this idiom taps into a broader motif at play in the story, as Billy isn't the only one of the narrator's family to have unrealistically optimistic ideas about his ability to repay the narrator. The narrator's daughter, for instance, always seems to think that things will change for her pretty soon. When she asks the narrator for money, it's always presented as if she's only requesting the funds for a little while, since things will soon look up for her financially. In both cases, Billy and the narrator's daughter seem overly confident that they'll be able to make things work—if, that is, the narrator simply helps them get through a brief difficult period. In other words, the idea of getting "out of the woods" looms large in the story, becoming a motif that highlights the out-of-touch optimism the narrator's family members seem to have about their ability to repay him.