Since it is also pitched as a means to create savings in public spending through cuts, possibly "cleaning up the tax code", I think it is going to be ideologically weighted towards this idea that it has an inherently limited scope because "we had to get rid of everything else to give you this free money, our hands are tied". But, assuming a significant amount of the workforce at some point actually becomes perpetually unemployed, which may not be true, it could create some interesting new class dynamics. If there is no realistic opportunity for most people to increase their income beyond the UBI, how is there any meritocracy or social mobility? The capitalist class in power at that point would be incredibly entrenched, born with more claims to property that have few believable suggestions as to how they may have earned that position, or how any of us could competitively threaten it such that they have proved their value as owners of capital. How does that change mass ideology about the economy being free, offering opportunity?
But if little else changes it seems that it would be more inherently friendly to the right. They'll get their cuts, most people will still work, and now they can always say that they are giving you free money, so why are you complaining? It will also be a continuation of the notion that privatizing is preferable, since you are in a sense privatizing your government programs by suggesting that the free money is money that would have otherwise been directed by the government, but now it is in your hands as a rational economic agent to decide how you will find all of those goods and services. There will be less reason to some people to doubt the meritocracy, because now you can also browbeat people for wasting their free money. I'm sure stories will abound about how some people used their UBI to start multi-million dollar businesses, while others just bought too much crushed avocado on toast.