The negative income tax really isn't a left or right issue, despite the fact it was advocated for by a free-market proponent.

The only problem I have with it is not the idea itself (I quite like it), but instead the income tax all together and the entire tax code. In the U.S. we waste a ton of money every year conforming to the tax code and there are many simpler ways that we could collect federal government revenue. I especially don't like the idea of taxing income. Something like the Fair Tax solves this but introduces a few problems as well. It would interesting if we could develop a system which functions like the negative income tax but has the efficacy of a sales tax.

BI has the advantage that it retains 100% of the marginal incentive to work at the low end of the spectrum. This comes at a marginal cost to the entire system, poor and rich alike, but arguably the poor need to be incentivized more than the rich.