If you want to do this, you need the data which proves that it can work in the USA.
Your argument amounts to: But, with a guaranteed income, people might refuse to do wage labor and would just live in the world going about their day following their interests instead of mindlessly processing meaningless bureaucratic forms in some office!
Indeed they might! There's a lot of work happening that need not happen. There's a TON of value coming from things you do not call "work." And your suggestion that having health and food and shelter should be dependent upon doing some miserable useless "work" is fundamentally corrupt perspective.
If less people work, there are less things being produced, period. If less things are being produced, there are less things to go around. If there are less things to go around, we are ALL less wealthy.
Is this decrease in wealth trumped by the increase in mental, emotional, and physical health which would supposedly occur under a basic income economy?
I don't know, and neither do you. It would, however, be relatively trivial to do some experiments, gather the data, and analyze that data.
It would certainly be preferable to do this than to dive headlong into a basic income scheme, only to find out that your posterior-derived claims are entirely false.
In any case, methinks your obsession with unemployment rate is one of the things that we must seriously reconsider if we really want to be objective about the merits (or lack thereof) of basic income (BI).
Let's get a bit philosophical here. One of the fundamental premises of BI is that it's OK for a substantial portion of a future society not to do anything that is traditionally considered "work". And one of the reasons we need to experiment with BI is to see whether or not this seemingly outrageous premise turns out to be correct after all.
Including the unemployment rate in your definition of "it can work in the U.S." is inherently biased against BI because it already assumes the opposite of one of the premises of BI. It's like trying to decide between theism and atheism using the Bible as your measuring stick. Regardless of what conclusion you draw at the end of the day, that competition ain't fair.
In order to make a fair decision, we'll need to go a little meta and ask, for example, about the total productivity of the society, the physical and mental well-being of its citizens, or something like that.
Thus, from a wealth standpoint, a system with less unemployment is preferable to one with more.
Proponents of basic income usually claim that when people are freed from the drudgery of working a normal job, they will be free to be creative, to take risks, to start businesses, and that this new productivity will compensate for the loss of productivity in the traditional system.
But that's all that is: a claim. It's completely worthless without some kind of data backing it up. It's akin to a preacher saying that God exists because he said that God exists. It simply has no merit.
So would the loss of productivity be compensated for by the increase in physical and mental well-being? I have no clue, nor do you, nor does anyone, because we lack data.
So let's get the data.
Once, my battery died and a paid a tow truck for a jumpstart. Another time, I was able to call a friend to get a jump instead. Both times the same service was provided.
The last time I moved, I paid movers to haul boxes. The time before that, my brother and I did the work.
Money in exchange for labor isn't the only way useful work gets done and counted. Some things will still get done even when people aren't paid to do them.
Or would our collective wealth (more broadly defined) be higher if those same people were creating works of art with their skills?
But that figure from Brazil is not the same as the unemployment rate so stop comparing apples and oranges. The figure from Brazil is going to include people on disability and old age pensions, etc.
Not everybody is on the Brazilian system, only people below a certain income level. According to http://www.bls.gov/cps/cpswp2011.pdf the employment level among those in poverty is something like 10%. Obviously you can't directly compare that to the Brazilian system without knowing more about how the US vs. Brazil define poverty, but it's obviously wrong to assume that all income levels are employed at the same rate.
Edited to add:
Per the CIA World Factbook, our workforce is 155 million, including the unemployed. Our population is 316 million, of which about 20% are under 14, and less than 35% are under 25. If we assume everyone under 25 is too young to work (which is crazy, but will give conservative numbers here) then we have 100% * (1 - 155/(316 * .65)) = 24.5% adults who aren't working or seeking work, which is right about the 25% in Brazil. If we assume everyone above 14 should be working (obviously overly aggressive, but for reference) we get 100% * (1 - 155/(316 * .8)) = 38.6%.