There have been experiments with NIT (Negative Income Tax) in the US. My impression was that they were a disaster, but in looking for them I found this article,[1] which explains some of the history of NIT in the US.
Negative income tax seems quite hard to administer when compared to a basic income. Why bother with all the bureaucracy required to deal with accounting for millions of minuscule incomes, when a simple flat payment would do the same job?
http://www.city-journal.org/2011/21_1_income-tax.html