in the fiat system of currency creation adopted with the Central Bank starting 1913, money, is relative as much or more to time as amount.
Spend or Tax the Government is just making data entries on their spreadsheet. Right Now! it is imperative that money be left in the hands of desperate people so they can pay bills, and buy what they need to survive. So Small Business can stay afloat and hire people. Immediate Activity! Not hands in the Pie in the Sky STIMULUS!
You are making the wrong assumption by listening to the oversimplified explanation.
The fed can "change the numbers on the spreadsheet", but only if they are able to undo the change later so that the effect is zero. It's like a temporary loan with the interest payments done under the table. It's not free money in the way that you explain it, and it can't be extended to giving away free money to people, like you propose.
The Recovery Act uses real money for the stimulus that is all accounted for. The money will be spent, so it is not temporary, and it cannot be undone later by editing a spreadsheet. That makes it completely different to what is done for the banks to maintain their solvency.