I just saw this article about whether the stronger European safety net means that they don't need separate stimulus packages. I don't really know how much spending is needed to turn their economies around, but would note that less than half of the American Recovery and Reinvestment Act could even vaguely be described as safety net spending (and only that much if you include all of the individual tax credits in that category).
But, I think the broader point, that the European programs are far more countercyclical the US programs (meaning that they automatically grow during hard times) is really important. There are a couple of reasons for this. The obvious explanation is that their social programs are far more generous than ours in general. But I think it's equally important -- although not as obvious -- that several of our major programs -- especially Unemployment Insurance, TANF, and Medicaid -- are administered at the state level. By constitution, most states aren't allowed to run budget deficits, so they're forced to cut services or raise taxes just when people need help the most.
The Federal government often chips in to help states when times are bad, but that requires specific legislative action, which often creates political complications. There's a program -- the Extended Benefits program -- that is supposed to provide extra unemployment insurance to workers in high unemployment states, but the mechanics of it are so messed up that in practice, Congress always comes in and passes a separate program. And that often happens well after we're in a recession -- the one good thing about this one is that it got people to pay attention relatively early. Obama's budget includes language about fixing the Extended Benefit triggers, which made this policy wonk happy.
The Times article that I linked to above mostly focuses on a German program called “Kurzarbeit,” or short-work, which allows firms to cut workers hours instead of laying people off, and the government makes up a portion of the reduced wages. There's actually a U.S. version of that in some states, called work sharing, although almost no one has heard of it. It's a good idea.