Here's a graph showing SNAP enrollment, along with the unemployment rate and the poverty rate. The decline in SNAP enrollment after 1996 is part of the aftermath of the welfare reform act that passed that year, which led to much smaller welfare rolls and also tightened rules for receiving Food Stamps. the run-up in SNAP enrollment since the start of the recession is large, but Andrews and Smallwood point out that it's within the historical parameters of what one would expect given the rise in unemployment rates and poverty rates over that time.
When you look at the numbers, Food Stamps play what may be a surprisingly large role in America's social safety net for the poor. Total spending on Food Stamps in 2011 was about $78 billion. According to the Center on Budget and Policy Priorities, "Roughly 93 percent of SNAP benefits go to households with incomes below the poverty line, and 55 percent go to households with incomes below half of the poverty line ..."
For comparison, federal expenditures through the Earned Income Tax Credit were about $56 billion in 2011. As another comparison, total spending on Temporary Assistance for Needy Families (TANF), what is what most people mean by "welfare," was about $33 billion in combined federal and state spending in 2010. In many states, SNAP far outstrips TANF in the level of support it provides for low-income families.