The tensions between responsible and responsive government have increased in the age of populism. How do politicians deal with this challenge? Do they give priority to short-term voter demands or are their strategies guided by the Weberian ethics of responsibility? We study this dilemma in the case of the Swiss popular vote establishing a constitutional amendment to cap immigration. This cap went against treaties with the European Union, which are of utmost economic importance to the Swiss people. We argue that politicians try to avoid a decision when facing a dilemma between responsibility and responsiveness to the people. If forced to take a stance, they may opt for responsibility, while shifting blame for being unresponsive to external scapegoats. Hence, politicians try to be responsive as long as possible before turning responsible and externalizing blame to minimize the electoral costs of non-responsiveness. This is a policy of muddling-through. Our findings bear important implications for representative democracy in times of external constraints.