Make the debt collectible.
Instead of minting a one trillion dollar platinum coin, mint 9 copies of a one-hundred-billion dollar platinum coin, 99 copies of a one-billion dollar platinum coin, 990 copies of a one-million dollar platinum coin, and 10000 copies of a one-thousand dollar platinum coin (it adds up to one trillion if I did my math right), and allow them to be purchased by collectors at face value plus the cost of the metal itself. If no one buys them, they stay on deposit with the federal reserve.
The power to coin platinum is meant for collectors, so just minting a coin as an accounting trick might not be kosher with the courts. The idea of selling collectible debt-limit coins neatly works around that concern and allows interested parties to collect a memento of this crazy time. If some multi-billionaire wants to buy a platinum coin worth one billion dollars just because s/he can? Fine.
The tea party has gold, the rest of us can have platinum.