The two reporters are looking for a (big enough) story that will boost their reputations and help them establish themselves as serious, well-known journalists; in other words, a "career-making story." When we say that something is "career-making," we generally mean that it was something that helped build someone's reputation as a professional and thus helped them establish their career. For example, you could say that the Harry Potter series was a set of "career-making books" for J.K. Rowling, since they helped her establish herself as a well-known, professional writer.