I'm personally pretty skeptical that it would indeed cost less than what we have. (I'm in Canada, but basically the same arguments apply.) I expect there would have to be a significant tax hike, which could be structured so that it cancels out the basic income somewhere in the middle class range, leaving the poor better off and the wealthy nominally paying more.
However, it could also achieve so much more than the current minimally effective (if that) safety nets. People would not be forced to take a job just to survive. They could instead pursue work that they enjoy, and most likely end up making a greater contribution to society. This would apply for the middle class as well. Rather than being so focused on compensation, people would have more freedom to pursue the job that gives them maximum satisfaction, again benefiting all of society. Sure, some few would just milk the system, but it's ingrained in human nature both to produce something of value and to try to better one's state in life, so I expect that would be the minority.
Even though I wouldn't directly benefit financially from a system like that, I would love to see it seriously explored.