According to Wikipedia, only the bottom quartile of the US population earns less than $22500 per household; if you assume that BI isn't simply added on tax-free to higher-earning households' net income, that makes it more like 1/4 of the 80% of the population over age 14 would be eligible for full BI benefits. So, call it 20% of your original population estimate.
That makes it roughly $600 billion, with the potential chance of largely replacing welfare ($532 billion* in 2013) and federal disability ($166 billion), not to mention some portion of Social Security and other programs.
Sounds like a reasonable idea to at least explore IMHO.
* per charts at usgovernmentspending.com