There's an interesting graph at Gates of Vienna showing workforce participation rates in Sweden.
Between 1992 and 2002 70% of native Swedes of working age worked full-time. For immigrants to Sweden from Western Europe the percentage falls to 55%. For those from Eastern Europe it falls again to 50%. For Southern Europe the figure was 40%.
And for migrants from the Middle East and North Africa? Only 25%.
So the claim that you need open borders in order to rescue the welfare state just doesn't seem to bear scrutiny. If anyone is doing any propping up of government revenues it's the native Swedes.