Welfare isn't a large part of the debt, I'm sure. But... uh wouldn't they get more money if they had the opportunities available to make more money? This isn't just about how much money is spent. But how much money they take in. I'd imagine their lives would be better with a job, than on Welfare. And then hey -- they'd have more money to spend.
The question is "how does he intend to do that?" It'd be great if more jobs existed and they paid better. I don't think anything Santorum would suggest would actually accomplish those things.