In recent years, all eurozone member states have introduced national fiscal rules, which put limits on public deficits and debt. Fiscal rules reduce the fiscal policy discretion of politicians and affect their capacity to use public budgets for macroeconomic steering and redistribution. While such institutional discretion constraints run against the traditional policy preferences of social democratic parties, it is puzzling why they supported national fiscal rule reforms during the European debt crisis. This paper argues that the concept of structural deficit rules, central to reform efforts across the eurozone, allowed for the formation of an ambiguous consensus between center-right and center-left parties. While conservative and liberal parties are generally supportive of institutional discretion constraints, structural deficit rules - in contrast to nominal deficit rules - allowed social democratic and other left-wing parties to link such rules with their broader policy preferences of Keynesian countercyclical policymaking and the protection of tax revenues across the economic cycle to ensure the state's capacity for redistribution. Drawing on three country case studies (Germany, Austria, France), this paper shows how the concept of structural deficit rules facilitated - at least discursively - the support for discretion-constraining institutions among social democratic and other left-wing parties. In theoretical terms, this study also advances research on the role of ambiguity in political decision-making, (re-)conceptualizing three forms of ambiguity underlying ambiguous consensus: textual ambiguity, institutional ambiguity, and ideational ambiguity.