Well those are big separate questions. First, it may surprise you to know that countries do not WANT to eliminate their debts. Those debts exist in the form of government bonds, and trading and holding government bonds are a very important part of the financial markets. Mutual funds invest in them, widows invest in them, corporations like Apple that have huge multi-billion dollar amounts of cash in their accounts mostly invest this cash in US Treasury Bonds. They are an important part of bank capital and an important part of how central banks help to manage the growth of their country's money supply and help to control inflation or deflation.
So in short, this is not like a person's credit card debt, which is basically seen as all bad (aside from teh cool stuff it bought). It would be totally undesirable for gov't debt all to be eliminated. Some countries would like to have LESS debt, but few countries would be interested in eliminating their bonds altogether. This is one reason neither the USA nor hardly any other country on earth will EVER totally pay off their national debts. A country's national debt does NOT need to be "paid off" -- ever.
Furthermore, though it's theoretically possible that a country might just create new money in an attempt to pay down its national debt, this would have horrible consequences. The rate of money creation must be contained -- if you create too much money too fast, the result is hyperinflation. Money is like anything else, its value is based on supply and demand. If you had an explosion in supply from rapid money-creation, the value of it would fall immensely ... the currency would become close to worthless.
Technically the bonds could be paid off (ie, bought back from bond holders), but from that point on the currency would be worthless, because the world would be awash in that currency, and the government could't buy anything more ... and the economy would be totally wrecked. A government that cannot buy anything is dead. And the hyperinflation could not be controlled, because the way to reduce money in circulation is for the central bank to sell government bonds to banks and to the public, to absorb the cash (ie, exchanging bonds, which cannot be spent, for cash, to get the cash out of the hands of the public.) But the central bank cannot do this when there are no bonds anymore.
Such hyperinflation has created famous historical economic disasters, such as in Post-World War I Germany, and recently in Zimbabwe.