I think you might underestimate the cost of services that address the extended consequences of basic poverty. There is lots of criminal enforcement, healthcare, housing, etc., that is disproportionally expensive to maintain due to the perverse incentives created by existing policies.
With basic income, the only people who would need additional services would be those with physical or mental illnesses which prevent them from being able to escape from squalor. Whereas today there are many people whose skill-set consists of many clever ways of exploiting the social programs that are intended to provide much-needed assistance.
Also, with basic income, there would still be taxation of that income so many blighted areas would begin to have a tax base for things like law enforcement and other important infrastructure.
When you consider that nearly half of Americans effectively pay zero income tax today (1), their productive output is very low and most of it goes directly into state taxes and payroll taxes (which are highly regressive).
So the accounting of basic income would necessitate removing the regressive shackles of payroll tax AND replacing the demographically unsustainable social security system with something funded out of general revenue.
The thing I like best about basic income is that it corrects for the political distortions caused by social security. The annual statements are expressed in highly misleading future dollars and the whole thing is a self-perpetuating shell game that nobody can count on.
But imagine instead a large number of voters of all ages who happen to have had to lean on basic income for some period of time in their lives. We'd end up with a system driven (politically) by empathy and experience, at least compared to the status quo when it comes to social welfare programs.
Imagine if everyone who ever took out unemployment insurance, had to consider filing for bankruptcy, ruined his/her credit score due to unexpected job loss, etc., could relate to the usefulness of having that basic income to fall back on.
There would be a huge impact on things like payday lending and all the gray market (or even black market) lending that victimizes the poorest among us. Suddenly a whole swath of minor organized crime vanishes.
Similarly, kids whose parents are unable to create a stable financial environment would have some degree of additional stability. Not to mention the reduced stress placed on the lowest earners. Studies show that low status work is among the most stressful things humans experience, and I would not be surprised if a lot of substance abuse and domestic abuse were reduced by the type of broad cushion that basic income provides.
Even Milton Friedman advocated for Basic Income, calling it "negative taxation" so that there would be a consistent incentive to work which lacked the distortions caused by typical approaches to welfare.
1: http://www.marketwatch.com/story/45-of-americans-pay-no-fede...