That would actually require a budget! 
My checking account doesn't require a budget. Each payday, my paycheck gets deposited into my account, giving my account a positive balance. I am then able to draw funds out of that account until they run out. When they do, I don't get to draw any more funds until the next payday.
The same is true for the US Treasury. Each payday, taxes are taken out of our paychecks and turned over to the Treasury. This is the limit (or budget) that the Treasury has to work off of. And when those funds run out, they can't pay anything else until the next payday. It is no different than what the average American faces.
The Executive Branch is in charge of the spending. They get to make the hard decision on what gets paid and what does not. It is their Constitutional obligation.