The result of the Referendum vote in the UK to leave the European Union did not only surprise observers but also underlined the importance of developing our understanding of how attitudes towards European integration are shaped particularly at a time when Eurosceptism appears to be on the rise. Drawing on rare and pertinent survey data collected before and after the September 2015 elections, in this paper we focus on Greece, which in 2015 came to the brink of exiting the Union, before a third bailout deal was reached with creditors that narrowly prevented such a forced exit. The paper explores the drivers of two kinds of support, specific (in or out) and diffuse support (further or less integration), allowing a comparison of the drivers of the two key dependent variables. To economic and political sophistication models, we propose a model inspired by the crisis management literature, which underlines the influence of framing contests on the severity, causes, responsibility and appropriate response to a perceived threat. Among others, we show that voters who believe that there is no alternative to austerity, as well as those that hold domestic actors responsible for the escalation of the crisis, are significantly more likely to support EU membership. Crucially, by all indications, we find that the crisis management model outperforms economic and political ones to explain support for the EU, suggesting that during turbulent times, the traditional predictors of support may be partially give way to shorter term evaluations of how well the crisis is being managed and by whom.