We would likely still have most of our people on some sort of welfare, but it would not be such a fiscal train wreck as their basic living costs would drop substantially. Sort of like an energy breakthrough that would make electricity so cheap no one would bother to meter it.
Just playing Isaac Asimov there, not trying to provoke a political backlash.
Never mind robots, we should replace all forms of welfare and gov’t social programs with a guaranteed minimum income.
Free markets for everything. No one starves or goes without health insurance. Armies of bureaucrats can now do useful work instead of administer welfare state.