This hasn't been true in decades. The people ("millionaires") who make ~150K/year pretty much spend all of it. It's the multi-millionaires and billionaires who make millions a year and don't spend that much, but those are the same people whose "income" is mostly unrealized capital gains. Switching to a consumption tax wouldn't materially reduce their taxes because they're not paying hardly any taxes as it is. (And getting rid of capital gains tax would increase economic efficiency because it currently prevents people from selling shares in order to buy better shares unless the advantage of the new shares can overcome the taxes due from selling the existing ones. Which would grow the economy and increase government revenue.) It's conceivable that a consumption tax would cause the super-rich to pay more taxes, because if you want the yacht you have to pay the tax, but there are currently a lot of tricks you can play to convert stock into stuff without paying tax, like selling only the shares that have decreased in value.
The best way to think of a basic income is as a fixed tax refund. A middle class person who pays $10,000/year more in taxes to fund a basic income and then gets the $10,000/year basic income it isn't actually any better or worse off than before.