First off children don't get the full amount only 1/2 which reduces costs by ~13%. $8500 / (1-.13) = 9770 / year which is rather close to 10k/year. A single person living on 10k after taxes is about the same as a single mother living on 15k hard but hardly impossible. If you add 10k per kid it creates a rather strong incentive to have a few kids.

Also, the assumption is you cut a lot of government spending not just social security. So unemployment insurance, HUD, food stamps, etc. While writing a SS check has vary low overhead handling disability is a huge part of the SS administration that goes away. And those programs are not all paid for by personal income so assuming all the other taxes stay the same you free up a fair amount of spending for the basic income.

Even just eliminating social security reduces taxes by 12.5%. And, presumably that $3,900 exemption for each qualifying child goes away along with the home mortgage tax deduction as do a lot of other deductions which can lower taxes for the rich who would otherwise be getting most of the additional tax burden. I would also suggest removing the deduction for charitable giving. (The only difference between deductions and spending is accounting the math is identical.)

PS: Actually finding the correct tax rate takes quite a bit of economic modeling 20% is reasonable ballpark, but you need to figure out what's cut to get a good idea of how that actually impacts people.

Spending on welfare programs is a tiny share of our budget. Add up everything -- state and federal -- and it's about 600bn from the data I've seen -- and before the recession it was half that.

Your comment about the 12.5% you save from social security should tell you what you need to know: In order to provide a "basic income" for JUST SENIORS we have to have a 12.5% tax. Now, nominally it's less, because social security taxes cap out at like $110k/yr so there are a lot of income dollars in the US above that amount that aren't paying Fica. Regardless, it's still a tax somewhere near 10% to provide about $15k/year to mostly just seniors. Disability and survivior benefits only make up 20% of social security.

I obviously looked up some facts here to test my assumptions -- everything is just on the social security website and usgovernmentspending.com

We give a lot more money than just 600bn to low income people though the tax code. (aka 10% income tax vs 39.6% income tax) Still 600bn / what amounts to ~275 million people = ~2,200$/person or 22% of a 10k basic income. Not to mention stipends for collage students etc.

  ~23.5% of the population under 18 get 1/2
  prisoners get nothing or close to it.

Also people can get close to 40,000$ from social security not just 10k.

PS: Only 65.5% of Social security goes to retired workers. Well over 63 million people get paid from social security but less than 40 million of them get traditional retirement benefits. http://www.ssa.gov/policy/docs/quickfacts/stat_snapshot/

The government currently spends almost $10K per child on public schools, so you can also shuffle in and out of that budget to make the BI cost for children "disappear" in your models.

So then to lift everyone out of poverty, we just need a 40% flat tax on top of the current federal taxes (so that we can continue to fund everything else). Hooray, 70% tax rate!