I first remember hearing the idea back in the late '90s in a course called "American Public Policy" that I took back in college, and my initial kneejerk response was to crap on it. However, we were required to study the policy justifications from both from Milton Friedman (who was following Friedrich Hayek's position) and Martin Luther King (who made it his top priority after the Civil Rights Act), and frankly both of them had strong arguments that made a lot of sense.
Link. Since then, I haven't necessarily jumped on board, but I'm at least receptive depending on the specifics.
Frankly I'm surprised we didn't adopt it in the late '60s or early '70s, and had MLK lived, I think there's a good chance we might have. Democrats weren't very enthusiastic about it back then, because they had just launched the War on Poverty and wanted to keep the focus on expanding those programs. Furthermore, because the War on Poverty was a top-down, centrally-planned and controlled gaggle of welfare programs, which was somewhat in conflict with the core principle of a UBI, which was economic empowerment of the individual recipient.
However, after the 1968 election, Nixon (who supported a UBI) was in the White House, and though the GOP didn't control Congress, it had a bigger and more powerful minority than it had had in several years. Had MLK lived, he very possibly could have helped build a coalition of Northern and West Coast Republicans and black empowerment liberals to get it done. The opposition would have been Southern Democrats and academically-oriented liberals (who were the big force behind the War on Poverty programs), but they may not have had the numbers ot stop it. It would have been a close call.