Among the central tenets of globalization is free migration of labor. Although much has been written about its benefits, little is known about the limitations of globalization, including how immigration affects the anti-globalist sentiment. Analyzing polls data, we find that over the last three years in a group of EU countries affected by the recent migrant crisis, the percentage of right-wing (RW) populist voters in a given country depends on the prevalence of immigrants in this country’s population and the total immigration inflow into the entire EU. The latter is likely due to the EU resembling a supranational state, where the lack of inner borders causes that ”somebody else’s problem” easily turns into ”my problem”. We further find that the increase in the percentage of RW voters substantially surpasses the immigration inflow, implying that if this process continues, RW populism may democratically prevail and eventually lead to a demise of globalization. We present evidence for tipping points in relation to the rise of RW populism. Finally, we model these empirical findings using a complex network framework wherein the success of globalization largely rests on the balance between immigration and immigrant integration.