The share of people who are very concerned about public debt varies a lot across countries. The magnitude of public concern for selected is show in this chart:
Data: Pew Global Attitudes survey, 2014
I posted the spreadsheet with additional countries on Github.
Looking at the EU only, the deficit was mentioned as one of two priorities by a substantial proportion of people in many countries, including some where debt sustainability was not an immediate concern:
Data: Eurobarometer (2010)