Paper money is fiat currency, but coinage actually has intrinsic metal value and is not the same as paper money. The US Mint sells silver and gold coins at or near FMV. For example, a One Ounce $100 Platinum American Eagle (1997-Present) contains 99.95% Platinum, weighs 31.12 grams, has a denomination value of $100, but a current melt value of $1,557.75. Its melt value would have been between $350 and $400 in 1997.
You can actually buy a $100 denomination platinum proof coin from the U.S. Mint today for just $1,892.00 (US Mint). Imagine that, a $100 coin for $1,892. So although the government could mint a wooden nickel and stamp a denomination value of $1 trillion on its face, its intrinsic value will always be the worth of its components.
I think the government should do it. The first time would cause a lot of comment and predictions of doom. The second time would precipitate the collapse and if the first time were perceived somehow a success there will be a second time.
The longer we put off the collapse the farther it is to the bottom and the less likely that we will be able to climb out of that abyss.