It’s actually simpler than all that. You don’t have to work it into the budget at all .The US can pay for a basic income through deficit spending. Basic income can simply come from additional spending.
A lot of people think this would cause too much inflation, but they’re wrong. Inflation only occurs when the rate at which money circulates outstrips the rate at which real wealth is being traded. But when new money is distributed in the form of a basic income, it causes us to scale up production.