The "mint a coin to pay the Fed" idea was popularized by Presidential Candidate Bo Gritz back in 1992. It was a huge part of his platform at the time, spoken about at every campaign stop.
From an old archive, so you can see the 1992 date:
And, if this only costs a cent to make, but they have to give us 25 cents credit, what is wrong with minting a giant coin (Bo holds up a 5" diameter, giant coin) that says "Four Trillion Dollars Debt of the United States Paid in Full In God We Trust." (Huge round of applause.) Now, I ask you, let's be very clear about it: is that legal? I'd be very enthusiastic if I thought I could get my great grandkids, my grandchild who's thirteen now and my three mules and a daughter, if I could get them out of debt because they all owe $42,000. That's what every one of you owe and that's what your kids owe and if you're born today, that's the price of being an American. I'd be excited about thinking on this because is this coin going to be made out of gold? Is it going to be made out of silver? No, it has to be made out of pot metal because it has to be worthless! It has to equal what it is that they have been giving us all this time!
From another source:
I appreciate your applause in our solution. But we've got to apply the solution, and that's something to applaud. You see, it has to be in pot metal, doesn't it? Because it has to equal what the value is of these things right here (cash). So if we made it out of anything that was either gold or silver, it wouldn't be fair, would it?
Now you doubt? You doubt this? Let me read you, because you see we said, gosh, if they have to give us credit for the coin's face value, no matter what the coin cost to manufacture or is worth, why don't we just pay off the debt? So we wrote this letter, and here comes the answer. By the way, signed by Mr. Monk, who I'm glad did it because he's a lawyer, Assistant General Counsel to the United States Treasury Department, "The former chairman," so this has been thought of before, but you probably never heard of it, "The former chairman of the House Coining Subcommittee correctly points out that we could pay off the national debt with a single four trillion dollar coin." And so we will.
Some people seem to think that the whole trillion dollar coin idea is of recent vintage, but history shows differently.
UPDATE: The Wall Street Journal issued a minor correction under the title "Send In the Clowns" updating the source of the idea to reflect Bo Gritz. Previously they pointed to a Simpson's episode from 1998.