I'm not interested in getting more "free handouts" for myself; I'm interested in helping others in need.
I also think that for many services (e.g. health insurance), government delivery can be more efficient than private delivery, so putting these things under the responsibility of the government can result in cost savings, meaning that there's more money to go around to do things like pay off the debt.
If you prevent a person from developing a debilitating condition, then you preserve his ability to work. This means less government expense (in the form of disability program payouts) and greater government revenue (since he's earning income that gets taxed). It's a win-win... as are many things in a true social safety net. Proper resources for the elderly means that their adult kids are freer to work at paid jobs instead of caring for their parents. Government-sponsored childcare can allow single parents to work instead of staying home and on welfare to make sure their kids are taken care of. Good public schools create a capable, technologically savvy workforce that can add value to the economy (while creating jobs and tax revenue in the process).
Most of the things in a social safety net are really "win-win" measures when you look at them in the context of the big picture.