In 1994, a Times-Mirror poll asked the same question and found 12% said better, 73% worse, and 9% volunteered that it did some of both. Although opinions were still predominantly negative in 2002, they were a lot less negative than they had been just eight years earlier.
Why? The welfare reform of 1996 was popular and well publicized, so maybe that caused the shift towards more favorable views. Still, my feeling is that a single piece of legislation, especially one that most people have no direct experience with, is unlikely to make that much difference. There seems to have been a strong conservative/anti-government mood in 1994, for reasons that aren't clear to me, and probably the very negative views of welfare reflect that (see my post on food stamps). Unfortunately, the question has not been asked since 2002.
[Data from the Roper Center for Public Opinion Research]