The European Commission has adopted an Entrepreneurship 2020 Action Plan as its answer to challenges brought by the gravest economic crisis in the last 50 years. Governments of European countries all habour high expectations that entrepreneurship will contribute towards ending the continent's economic malaise. In this article I argue that these expectations may be disappointed because (i) entrepreneurship promotion is a last-resort policy, (ii) entrepreneurs are being overestimated, and (iii) entrepreneurs are too often allowed to capture policy. These reasons are indicative that that in addition to its euro and refugee crises, Europe is suffering from an entrepreneurship crisis. Entrepreneurs are increasingly older and are faring less well in terms of earnings compared to wage earners. Small businesses are not creating sufficient jobs, they are not raising labour productivity, and immigrant-entrepreneurs are not productively assimilated. Big businesses are largely a legacy of the past, and resorting more and more to lobbying. When they innovate it is often to replace labour. Hence, given that Europe faces rising unemployment, growing numbers of unassimilated migrants, and more pensioners - and all in the face of stagnating productivity growth - the conclusion is that entrepreneurs have failed to reduce the dependency burden on those who do work. This puts immense strain on European public finances that are already fragile after the financial crisis. Demographic changes and institutional shortcomings are thus at the core of the entrepreneurship crisis in Europe.