No, by counterexample of USA.
The 2015 average income per capita was $57,540 [0]. The 2015 poverty guideline for a family of five was $28,410 [1]. Clearly there is more income per capita than required to keep everybody out of poverty.
A second source, the Census, is pretty reputable too: "Median household income in the United States was $56,516 in 2015." [2] Edit: This statement isn't helpful since it is a median, not a mean. A better source from the Census is [3], which lists the mean average as $75,738. As a reply pointed out, the heavy income inequality in the USA is expected to cause this sort of skew in the median.
Either way, I propose that taking everybody's income away and then splitting it evenly would apportion enough money to keep everybody out of poverty, that it would be sustainable (based on trends of past amounts of income per capita and poverty guidelines), and that it would clear the poverty guideline, a well-known bright line for "basic life necessities."
Is this a good solution? Maybe. There's probably better ones. But they do exist.
Edit: Specifically, would this system remain stable? It's hard to say. We can imagine that anybody on the sad side of the Pareto curve, which is a majority of the typical employed people in the USA, would not mind effectively having a big check from Uncle Sam raising their income to healthy levels. At the same time, we could also imagine that the wealthy few who are hit hardest in this scheme would try to find some way to get their income to be non-taxable, whether by lobbying for a proportional tax or inventing new capital transfer techniques. I'm not going to claim that this scheme is in any way socially workable over the long term, though. I personally feel that any UBI scheme is still socially unworkable; we need more small-scale evidence that UBI works.
Still edit: As an example, imagine that the UBI payments were only sufficient to bring the impoverished up out of poverty, and not necessarily any higher. That means that over half of the income marked in my original scheme would not be needed, so the wealthy could keep it. This would effectively be a two-tax-bracket system, with the brackets labeled "below" and "above." Does it still work on paper? Yes. Do I think that people will like it? No. Do I think that people like taxes? Not really.
[0] http://data.worldbank.org/country/United-States
[1] https://aspe.hhs.gov/2015-poverty-guidelines
[2] https://www.census.gov/library/publications/2016/demo/p60-25...
[3] https://www.census.gov/data/tables/2015/demo/cps/hinc-06.htm... (Warning: XLS sheet!)