Sir - you are describing a simplistic zero order differential effect on the economy. Your reasoning might make sense in test tube isolation. Unfortunately, there are huge volumes of "cash" commitments tied up in an amazing number of bizarre leveraged derivative instruments. $300 - $400 Billion is responsible for over $1T in differential products - the number and variety exposed grows every day. Not to mention the higher order multipliers involving retail sales and services to home owners, factory orders, food, commodities, futures markets, foreign debt servicing, etc.
No - this is not overblown. I can hardly wait for my $200 check from the great bush. It will be nice to finally have a full tank of gas with some left over for a gallon of milk, load of bread and a dozen eggs.
As the great GW Bush said - "core inflation is low, except for food and energy...". Ahahahahahahahahah - he should have paid more attention in his economics 101 class. I guess he was too busy cheer leading!