The main issue in Denis Johnson's "Car Crash While Hitchhiking" is responsibility and helping others. The story's narrator, a young man, tells of a car accident he was in. A family from Marshalltown gave him a ride during a storm. The narrator had recently gotten out of another car, and he had large amounts of drugs and alcohol into his system.
The narrator comes across a family while "something less than conscious," and he believes that there will be a horrible accident (apparently, he can glimpse the future). He accepts the ride while knowing that the accident will happen. Not caring that the accident will take place, the narrator gets into the car because the family agrees to take him all the way to his final destination.
After the accident, no one seems to want to take any responsibility for either the accident or the aftermath. The man driving the car denies the accident. The narrator denies the wife's death. The truck driver, who happens on the accident, does not want to go for help, stating that he cannot turn around where he is at. He also refuses to take the baby, but he does agree to allow the narrator and baby to sit in the cab until help comes. Lastly, the narrator ends up in the hospital, refusing treatment.
The story then jumps forward in time to several years later. The narrator is again in the hospital, this time due to drug abuse. The story ends with the narrator speaking directly to the reader: "And you, you ridiculous people, expect me to help you."
Essentially, the issue lies in people not taking responsibility for their actions. It also lies in people not wanting to take responsibility for things that they do not find necessary (like a car accident involving others).
Superficially, one could also argue that the issue of the story lies in drug abuse and the ramifications which arise because of drug abuse. Given that the closing situation revolves around the narrator's drug abuse, one could easily state that drug abuse is an underlying issue raised in the text.