I might be persuaded to do that, if it meant that pretty much all social programs go away, and that a lot of laws, agencies, regulation, subsidies and even military spending were cut. With a target of cutting the federal budget by 70%. If course it feels like I have that much coming out of my paycheck already.
1) Even if the marginal tax rate is fairly high, your average income earner will be getting that $18000 back in UBI which makes the effective rate in your scenario more like 5%.
2) The majority of tax revenue comes from the highest earners. A quick google gave me this (from https://taxfoundation.org/summary-latest-federal-income-tax-...):
The top 1 percent (1.3 million filers) paid a greater share of income taxes (37.8 percent) than the bottom 90 percent (124.5 million filers) combined (30.2 percent).
In other words, I don't believe your math is a reasonable approximation of how the budget would work out. If everyone pays the same effective rate as today (including welfare and other social program recipients who can be treated as having a negative effective rate), nothing changes. Also, there is no need to presume a flat tax rate; the U.S. does not have a flat tax rate, now.
EDIT: Also the average household size in the U.S. is 2.53 people, not 4. A naive calculation would suggest that a household of 4 should therefore expect a mean income around $83K.
No, of course, I would not propose that. There are many ways to handle it that effectively amount to the same thing. The UBI could be paid out monthly or fortnightly or whatever seemed good with the tax situation otherwise being the same. Your employer would have to withhold a bit more tax to compensate, but the end result would be the same.
The point is not to argue specific implementation details; it is to offer another way of thinking about it.