The way most universal basic income schemes work is that the government provides everyone in the country with some amount of money that meets the minimum requirements for living, usually either through a negative income tax or (my preferred solution) simply cutting everyone a check. Such a system would entirely replace existing forms of welfare, social insurance, and government incentives (such as tax breaks for things like having kids).

A basic universal income seems to be to be manifestly superior to the system we've got now. Many welfare systems are riddled with corruption, paternalism, and incompetence. The USA has a confusing and overlapping system of over 100 different agencies providing some form of social payments or incentives. People think of "welfare" as a thing the government does for the poor, but by far the most significant benefits go to middle and upper class families, often at the expense of the poor (thinking specifically here of Social Security, a tax on the young and working poor to pay for the relatively more well-off aged).

If you did it the easiest way possible, eliminating all non-business welfare, social insurance, and tax systems, and replacing them with a single monthly check perhaps determined by 150% of the poverty level in the citizen's resident county, then the government could just use the existing Social Security Administration infrastructure. I'd probably add some federally-insured health coverage with a very high yearly deductible, perhaps $10,000; this would allow for a market of relatively low-cost supplemental insurance that high earners or the relatively young and healthy could go without. A sufficiently progressive income tax would solve the moral dilemma of the government paying money to the extremely wealthy (which goes on all the time anyway and nobody seems to care).

I've seen various estimates about how much a program would cost, to being slightly more than the existing American welfare system to costing much less, thanks to the reduced need for bureaucracy and the gains from things like eliminating tax breaks or new efficiencies like decoupling health insurance from employment. But even if it cost slightly more, the gains from streamlining the system and eliminating the human costs of our current system would be well worth it.

As best I can see, the strongest argument against a basic universal income is that it would be practically impossible to put into place. Too many people benefit or think that they benefit from the current system. But given the absolutely messes that constitute the current welfare systems of the big western countries, I think there would be a public interest in it.