I also think most BI supporters tend to shoot too high. The equivalent income of just a 16hr per week job at min wag would do wonders for the economy without putting a great deal of pressure on people not to work.
[1] http://www.usgovernmentspending.com/year_spending_2015USbn_1...
You could also probably greatly simplify the tax code, which has become a form of welfare with the poor paying less and the richer paying more relative to the amount they earn.
Then there's other potential benefits or reductions in cost, that are harder to quantify and predict. Would there be a reduction in crime? (which could reduce police costs) A decrease in sickness and health costs? (due to increased nutrition and better shelter) An increase in productivity and a boost to the economy? (due to people being in better health, being able to get more education and a tax code and welfare system that doesn't incentivize making less) What about all the non-profit organizations that spend millions helping the unfortunate? (What could that be spent on instead?)
I'm not necessarily in favor of a basic income to the extent mentioned in the article. I do wonder, however, if some limited basic income could be more effective than our current programs designed to help the poor and needy and if it would provide some better stability in people's lives generally. Either way, it would have a broader impact on the economy than simply removing welfare programs from federal and state budgets.
"Eliminate" would never fly politically, and to be honest I don't think it's the right thing anyway. We probably could reduce/consolidate, if we did so in a way that meant (BI + SSI) was never lower than SSI before the change, which would certainly still mean savings.
The argument for a basic income is that one should be able to live comfortably and not just cover bare essentials. This means that people shouldn't be living at the poverty line but well over it. This shouldn't be a disincentive to work because most people need to live their lives around some kind of structured activity. Though it does mean that if there is a shortage of jobs then the unemployed won't be left to rot and the option exists to do some meaningful volunteer work.