The fact that Tom's wife, Sallie, has a good job as a doctor rankles this macho Southern male. Like many men in his position, he feels emasculated by his wife's success, a situation that's compounded by his own chronic inability to find work. It's not that Tom's lazy—he's applied for literally dozens of jobs. But all he's ever received for his troubles is a large stack of rejection letters.
As Tom admits, he could've taken a job collecting funeral insurance premiums from poor African Americans who just wanted a decent burial. But he didn't want to do such a soul-destroying job, so he remains unemployed.
Besides, it's not just Tom who's holding himself back from getting a job. As we're made constantly aware throughout the story, he's carrying around a lot of baggage from his troubled upbringing. The Wingo name is a burden to Tom in so many different ways. The Wingos have a notoriously bad reputation, and it's largely because of this that Tom can't get a job in South Carolina. Too many people in South Carolina know the name Wingo and don't like what it stands for. Tom wants to make a clean break and leave his life in Charleston firmly behind him.