The Trillion Dollar Coin

Recently I was reading an article about the proposal to mint a one trillion dollar platinum coin to be used by the government to pay off its debts and avoid a financial catastrophe. In the comment section someone was arguing that you can't just mint a coin and assign it a trillion dollar value. Upon reading that, I was reminded of the old story of the well-dressed man who approached a young woman and asked, miss would you sleep with me for a million dollars. She looked at him for a moment and then said, yes, yes I would. He then asked her if she would sleep with him for $20. Indignantly she responded, NO, what kind of girl do you think I am? He responded, we have already established that, now we are just negotiating a price.

To those that think that minting a trillion dollar coin is absurd, how is that different from what the Federal Reserve does today? They simply create dollars out of thin air with nothing to back them but the faith and good name of the United States of America. A Federal Reserve note is worth a dollar only because the government says so. If the government mints a trillion dollar coin and says it is worth a trillion dollars, how is that any different?  Would it be more acceptable if they minted billion dollar coins, and used 1000 of them to satisfy a trillion dollars in debt? Or maybe a smaller million dollar coin, then use a million of them for a trillion. Looks to me like we just need to negotiate a price.