Every dollar note comes into existence through one of the twelve Federal Reserve Banks loaning out money at a particular rate. Only those notes can be used to pay off the debt with a particular Federal Reserve Bank. So essentially this "money" is created out of thin air, and then loaned out into society.
Then that "money" is further expanded in private banks through a practice called "fractional reserve banking". According to the New York Federal Reserve Bank,
"If the reserve requirement is 10%, for example, a bank that receives a $100 deposit may lend out $90 of that deposit. If the borrower then writes a check to someone who deposits the $90, the bank receiving that deposit can lend out $81. As the process continues, the banking system can expand the initial deposit of $100 into a maximum of $1,000 of money ($100+$90+81+$72.90+...=$1,000)."
According to private sector calculations(since M3 is no longer released by the Federal Reserve) there is estimated to be 14.6 trillion reserve notes(actual dollar bills) in circulation today(a significant amount of that is being held by foreign countries so in reality, there is even less being circulated in the U.S. economy). So this provides a potential of there being 146 trillion dollars in total money after money expansion through "fractional reserve banking".
Every time the money supply increases, it pushes prices up. Let's say you grow corn. If you produce 100,000 bushels a year at $2.12 per bushel, you make $212,000 in gross sales in which you then deduct costs to determine your income. However, there is a limited amount of corn you produce. You cannot just decide one year that you will produce 200,000 bushels with the same amount of land and labor put into it. So each bushel has a real value as land is limited and your labor and time is limited. So if the government borrows one trillion dollars from the Federal Reserve and they then spend 100 billion on corn, there is now less corn that year and the usual purchasers, such as cereal factories, etc, now have to pay a higher amount to buy the same amount of corn as they would have before since the supply has been decreased. So the price rises and we see inflation. Then as the private banks expand that one trillion dollars to ten trillion dollars, the price of corn and other commodities will continue to rise(or one could say that the value of the dollar has declined).
So if the money supply is expanded through debt creation, which results in inflation, then when you try to pay off debt, the money supply will in return contract, which will result in deflation. So when any significant amount of debt is paid off that is more then being created at a given time, this will cause there to be up to ten times less the amount of money that is paid off. So if the United States Government paid down all of it's debt today, which is 9.3 trillion, this would cause the money supply to contract by upwards of 93 trillion dollars. That would mean a 64% decrease in the money supply. So the price of everything would then need to decrease to 1/3rd their current value(payroll included). During that adjusting period, very few things would be exchanged back and forth which would translate into many people losing their jobs and taking very large pay cuts and also not being able to purchase the basic amenities as they are priced 64% too high. People would feel like they just don't have enough money. Companies wouldn't have enough money to pay their employees and many jobs that are currently paid below 17$/hour would need to be adjusted below the minimum wage rate.
This would translate into a recession the equivalent of the Great Depression. Likewise any amount of paying down the federal debt will cause this deflation to occur proportional to the amount being paid off.
