So exactly how is minting a single coin valued at one trillion dollars different from just printing one trillion dollar paper bills?
It's different because Congress passed a law allowing the treasury to mint platinum coins in whatever denomination it wanted -- with no limit. There is no such law for any other kind of currency.
The law was a small measure intended to allow the treasury to mint collectable platinum coins. This actually generates revenue from coin collectors who buy such things.
Exploiting this law is a political stunt. If I were Obama, I'd be really worried about this backfiring. If they do the coin stunt, it will almost certainly end up in the courts.
On the other hand, there is some worry that it won't backfire and that it will be look upon as a "bold" move that Obama had to take because Congress is completely gridlocked. I think we can all agree that this would be a seriously bad outcome.
Any chance it'll cause our credit rating to get cut?