We could give everyone a UBI of at least $5k today, possibly even $10k, without costing anyone an extra dollar. There may or may not be moral hazards, although recent surveys from Sweden suggest that these are not as bad a people initially think. And this might sound harsh, but the sort of people that would stop working after receiving a $5k or $10k UBI are probably not really contributing that much to society anyway, so it might not be that big of a loss to the rest of us if they drop out of the economy.
But anyway, here's how the math would work:
The population of the US is 319 million.
Of those, 122 million pay federal income tax (source: https://www.reference.com/gove...)
Suppose that for those 122 million people, we gave them a tax hike of exactly $5k
Under a UBI, they could get an extra $5k, which exactly offsets this tax hike
So there are 192 million people left
Keep in mind that UBI replaces existing welfare payments, like social security and food stamps
Social security taxes bring in $920 billion (source: https://www.ssa.gov/oact/STATS...)
Food stamps cost us $74.1 billion (source: http://www.fns.usda.gov/pd/sup...)
That's enough to pay just over $5k to each of those remaining 192 million people
I haven't bothered to look into how much we're spending in admin costs to apply means testing to these welfare systems, and I haven't looked into how much money the various state governments are spending on various welfare schemes - all of this would become unnecessary under a UBI.
However the Cato Institute has looked into this, and they think we're spending $1 trillion per year on "welfare" (source: http://www.cato.org/publicatio...). I'm not sure I fully trust their analysis, but I'll take this as an estimate of the upper bound of what we could afford. So this, combined with social security revenue, would add up to $2 trillion per year to share amongst the 192 million non-taxpayers, which would give a UBI of just over $10k.
No need to tap into our Medicare funds, or cut any of our other expenses. We could continue to pay medical expenses, pensions, fund NASA and wage unnecessary and expensive wars around the world.
So that's where we're at today. In the future, there could be technological advances that make us more productive, and mean that we can lower our labor participation rate. The OP asks us whether UBI is the way to go in the future, and I'd say it's a plausible option.