The dynamic (converting universal benefits into means-tested benefits) happened 2 years ago in France with universal childcare benefits ("allocations familiales"). It's true that people weren't happy, but the pressure in favor of austerity was just too much and it was implemented very gradually.

It hasn't happened to Social Security because, if I'm not mistaken, the pension amount is proportional to what you earned during your career => hence the rich pay more but also receive more. Same with unemployment benefits.

This is actually the only way to make a universal monetary benefit politically sustainable. And UBI, with its fixed amount, doesn't match that criteria.