I voted to keep it, but only because I think the basic idea--that human beings who form a society should help each other--is right. I would run things very differently. First, I would make welfare mostly an employer-of-last-resort program. I can think many thousands of tasks that need doing all over the country, and which would generate economic benefit. If you require welfare in my (admittedly imaginary) nation, I will feed and cloth you and your family, and I will provide shelter and medicine. But you should be willing, in turn, to do work. I'll find something for you to do, I assure you. And more importantly, there won't be any stigma attached. You'll have a job, and you'll be producing value for everyone else in society. Now, there are many common-sense caveats. For example, if you're a single woman who is pregnant, or a single mother, you'll get a little more consideration. However, I would make it a crime punishable by a severe sentence for someone to take unfair advantage of this kind of generosity...
Second, I would reprogram education so that we go back to much more conservative models--we should drill students in mathematics and the classics before anything else. While this may seem unrelated, I suspect very strongly that students prepared by such a program will find their own sense of integrity and honor. And when you have a society of people who have integrity and honor, the applicants for welfare will, in 99.99% of the instances, really need help, which they won't use any longer than necessary.
Third, I would also reprogram education so as to make sure that everyone living in the U.S. should think of themselves as being part of a nation. Let's make it so that liberals and conservatives remember one basic fact: that we're a lot more alike than we are different. Ask any liberal and any conservative drawn at random on the street what they would do if they saw a person beating the living crap out of a defenseless infant, and the vast majority would agree that they won't just ignore it. They'll intervene, and/or call the police. I think most of us have forgotten them simple fact that we're generally decent folk, and that, perhaps, we can start there to find common ground. If we can do that, welfare programs will generally be used by people who really need our help, and who have in the past supported themselves, and in the future, will again.