Indeed, in the UK we have a personal allowance of around £10k of income which is not taxed. If you either remove that allowance or add the UBI to your earned income (same answer), you collect a lot more tax and the budget is now higher.
I think we have to be clear though, we are expecting to have to increase taxation to pay for UBI. If the need for UBI is driven by automation removing jobs, then the extra wealth that the automation creates is going to have to be re-distributed. It is also time to revisit the special treatment that capital (especially land) gets in the tax system. Land Value Tax is perhaps a much more socially aware approach.
I think we have to be clear though, we are expecting to have to increase taxation to pay for UBI. If the need for UBI is driven by automation removing jobs, then the extra wealth that the automation creates is going to have to be re-distributed. It is also time to revisit the special treatment that capital (especially land) gets in the tax system. Land Value Tax is perhaps a much more socially aware approach.