These are complicated issues. For example, what came to be called AFDC (the primary former welfare program) was actually first included in FDR's Social Security Act (the New Deal), later separated to focus on the specific needs of young families in poverty. The Clinton administration ended actual welfare aid (TANF is a short-term, marginally subsidized job program, only for those with children). Little attention was paid to the fact that Clinton also began similarly "reforming" Social Security as well, targeting the disabled.
I think the US is simply reversing history. The Great Society grew directly from the New Deal. It was necessary to end that, before we could begin dismantling the New Deal. The agenda goes well beyond the poor alone, of course, as we've seen the steady phasing out of labor unions for years, for example. I read recently that only roughly 10% of workers still have union representation. We've been racing back to the 1920s, setting the stage for the Great Depression ll.