Is it possible to eliminate the U.S. national debt? A political science teacher of mine has said that the U.S. national debt has grown way beyond reach and is now just a political talking point with no real value.  He says that there is no point in trying to pay it back and that it should be left alone since all the money is fiat, thus "imaginary".  What's your take on this?  Is it still possible to pay off the debt in 'x' amount of years without experiencing hyperinflation?
Yes, I imagine there's reason to contest that claim. Consider the GDP to debt ratio. While it has risen over time and with the recent recession, it was not too far away from Germany which is considered, I think, the absolute picture of fiscal health.

Consider also the critical point that the US government does not have a chance of death like a normal citizen. For example, if you take 30 year loan from JP Morgan, they consider the possibility that you might die. It is critical that they acquire this money before that happens- or they will lose their investment! The government does not have such concerns, and as a result face supernaturally low interest rates. Furthermore, they can pay back debt at a leisurely pace, extend their debt frequently, and if the interest rate is below the rate of inflation (Which it has been!), then they actually earn money by waiting to pay it back.

One of the main reasons for the increase in the debt-to-GDP ratio has been not an increase in spending, but a noticeable decline in government income.  The US tax rates are at historic lows. Even worse the US GDP has been smashed by the recession. The debt could be paid back eventually if it were politically feasible to raise taxes while keeping expenditures constant. The banks of the world have bet billions, trillions if you count derivative and second-stage investments, on this feasibility.

Finally, despite the fact that it is fiat money, it would be very unwise to act as if the debt didn't exist.  Note the panic over congress's threat to default. The consequences of even contemplating a default included: higher future interest rates, lower GDP, and  typically, a devalued currency. Conversely, if money is printed to cover the debt, the consequence is hyperinflation, leading to widespread drops in the standard of living. In my estimation,  if the United States did go into a spontaneous and total default, or hyperinflated to pay the debt- this would likely be the greatest economic disaster of all time, given the size of the US GDP currently. This is not hyperbole- I do not think there is a serious macroeconomist who would disagree.