Many studies have shown that individuals who interact with government programs subsequently participate in politics at levels different from before, whether higher or lower. While most prior work examines the effect of policy recipiency, or program administration in one geographic location or at one snapshot in time, I study how the administration of Medicaid, a federal program administered by states, varies over time and by place, and how its variation in administration affects mass-level voter turnout. I argue that there are two highly salient sites of contact with the administrative state when considering effects on voter turnout: government programs and elections. I theorize that administrative burden from these sites creates interpretive effects on both those with direct public program experience and those whose experience is indirect, which shapes the likelihood of voting. Using a generalized differences-in-differences design and applying my separate, original measures of Medicaid and electoral burdens, I find that having a higher level of Medicaid burden resulted in a small but significant decrease in county-level turnout in recent national elections, net of Medicaid expansion status, burdens associated with registering to vote and voting, and other factors. These results imply that contact with the administrative state, via government program administration and elections, is a critical way in which policies shape mass-level political participation.