From the right: F.A. Hayek, another right-leaning Nobel-winning economist, also supported a universal minimum income (not a negative income tax, but similar, of course. He also added a caveat that he thought it should be implemented IFF it was implemented everywhere).
I like the idea because it doesn't involve eliminating market economies. It's kind of like food stamps, but for a broader array of things: You can competitively purchase basic goods and services, which generally drives down costs and drives up quality.
From the left: One big concern with cash transfers is that some goods are complicated for consumers to understand (healthcare, for example). So, if you are left-leaning, maybe you can support a universal minimum income because the government could have a big role to play in, say, acting as a neutral agent and creating web portals and apps that efficiently disseminate excellent and easy-to-understand information about the types of healthcare plans available for purchase.