To put it in the most simplistic way possible, MV = PY.
Things get a little hairy when you get down to specifics, but any (and every) economist will explain to you that a rapid increase in the money supply yields hyperinflation. See Weimar Germany, Zimbabwe, etc., as historical examples.
Whether you're talking about expanding M by a trillion+ to deal with one year's budget (to avoid default) or paying off all your debt (19 trillion), you're talking about a rapid and huge increase in M. That's a suicidal maneuver as far as our overall economy goes.
I asked you to define "printing money" because the generally accepted definition is when the Fed buys U.S. bonds and not the public. This results in dollars, not bonds, being added to the private sector. Some people think it makes a difference; I don't. Either way, deficit spending results in an increase in financial assets for the private sector, and an increase in liabilities for the government. (I count the Fed as part of the government.)
"Paying off" the debt would simply mean exchanging dollars for bonds. If you are a bondholder, does this really change your situation? One day, you hold $1 million in bonds, the next day you hold $1 million in dollars. The tiny bit of interest you were earning from bonds probably wasn't enough to keep you from spending your money if there was something you wanted to buy, and it probably wasn't enough to keep you from investing in something riskier but more lucrative. So were the debt to be converted to dollars, it's not like everybody's pockets are suddenly full of new money that they are going to rush out and spend. If you had $1 million in bonds before, you could have liquidated and spent your million with minimal trouble,
but you didn't.
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The biggest problem with MV=PY is that Y changes. The other problem is that V is a derived figure, not a measured one. The assumptions necessary to make an increase in M => a corresponding increase in P make the equation worthless in the real world. Y doesn't stay constant, and V isn't constant, either.
Most examples of hyperinflation can be traced to a large drop in production and/or excessive foreign debt. The Germans not only had their productive capacity damaged by WWI, they had war reparations to pay for. We took their gold, and we took too much of their production. So they purposely started paying the victors with printed money. That is not a normal situation.
Zimbabwe dismantled their big, productive farms and redistributed them to people who had no idea how to farm. So their production went way down, and they went from exporting food to importing food. Their problems didn't come about because they decided to print a bunch of money - that came later.
A rapid increase in the money supply would not result in inflation unless demand outstripped the economy's ability to meet that demand. So you first have to ask, how are we increasing the money supply, and who is getting all of this money? It might get spent on food, or it might all end up in the stock market. Or, depending on what you count as the money supply, it might just sit around as reserves and do nothing at all.