Do political parties influence opinion when citizens have a personal stake in policy? With an experimental design that exploits a naturally occurring, sharp variation in party cues, we study the effects of party cues during a collective bargaining conflict over the salary and work rights for public employees in Denmark. Even in this context--where the self-interest of public employees was strongly mobilized and where their party went against it--we find that party cues move opinion among partisans at least as much as in previous studies. But party cues do not lead citizens to go against their self-interest. Rather, we show that party cues temper the pursuit of self-interest among public employees by moderating the most extreme policy demands. These findings highlight an unappreciated potential of political parties to moderate--not fuel--extreme opinion.