This paper explores opportunities and challenges for data-driven advocacy to support home care workers, an often overlooked group of low-wage, frontline health workers. First, we investigate what data to collect and how to collect it in ways that preserve privacy and avoid burdening workers. Second, we examine how workers and advocates could use collected data to strengthen individual and collective advocacy efforts. Our qualitative study with 11 workers and 15 advocates highlights tensions between workers' desires for individual and immediate benefits and advocates' preferences to prioritize more collective and long-term benefits. We also uncover discrepancies between participants' expectations for how data might transform advocacy and their on-the-ground experiences collecting and using real data. Finally, we discuss future directions for data-driven worker advocacy, including combining different kinds of data to ameliorate challenges, leveraging advocates as data stewards, and accounting for workers' and organizations' heterogeneous goals.