Since bypassing Congress to mint the coin is an inherent middle finger to Congress, most of the suggestions so far are aimed at provoking the House GOP as much as possible. To this end, Paul Krugman suggested using Speaker John Boehner's face for the coin, "because without him and his colleagues, this wouldn't be necessary."
On the other hand, you could just cut out the middleman and put Paul Krugman on the thing.
If maximum trolling is your goal, Obama is best off going with Sandra Fluke. For whatever reason, nobody in America prompts a more visceral reaction on the right than the young reproductive rights activist.
Rep. Greg Walden (R-OR) was so upset with talk of a platinum coin that he drafted legislation to ban the White House from minting one. So naturally he's a perfect candidate to go on the thing.
As the patron saint of absurdly epic (and epically absurd) policy solutions, Newt Gingrich deserves serious consideration for the $1 trillion coin.
If Obama is still sore over that whole first debate, this is the way to get it out of his system.
Who better to announce a coin worth one trillion dollars. Muahahahaha!
He's on a million commemorative coins already. How could any self-respecting Republican oppose putting him on the most famous one of all time?
Vice President Joe Biden appears to have a calming effect on fiscal negotiations, so sticking him on a coin might help smooth the way to a deal.
Update: The NRCC suggested on Wednesday that a $1 trillion coin was ridiculous, because it would take way too much platinum to mint.
In fact, the coin can be whatever size the treasury decides because America uses fiat money, meaning its value is not determined by the cost of the materials used to produce it. This explains why you don't need an entire bookcase to hold your $100 bill or why the guy at the deli who sold you a coffee this morning didn't weigh your quarters on a scale before giving it to you.
That said, the NRCC's suggestion offers a great design for the $1 trillion coin. Since the image isn't to scale, feel free to imagine the below coin to be whatever size you prefer.
Thanks to Jess McIntosh for the text.