The president is, right now, in control of the debate about the debt ceiling. He is not in control of how the conflict with House Republicans, which is really a conflict within the House Republican conference, will end. In theory, the U.S. treasury could simply print money equivalent to the balance between the amount Congress has authorized the government to spend and the debt-conditioned "ceiling" imposed on such spending by Congress. The U.S. dollar is not tied to any particular piece of metal, or "specie," and while minting a platinum coin and injecting it into the system (thereby allowing the Treasury to spend what it has been authorized to spend) could be inflationary, it is essentially a fairly neat solution to a problem that shouldn't be there in the first place.
Reports suggest the Federal reserve offered some technical reservations when asked about the idea, and the Treasury Department then concluded that it did not have the authority to actually mint the coin. Maybe.
The real reason the administration probably wouldn't employ the coin even if they really believed they could lies in the debate between Paul Krugman and Jon Stewart. It's not the details of the debate. It's the debate itself. Krugman thinks it can and ought to be done. Stewart ridiculed it because it sounds ridiculous. (Krugman responded; Stewart responded to the response.) The satirist's initial instinct was visceral. A coin? Really? It sounds too good to be true.
The moment the administration embraces the idea of a coin is the moment that the coin becomes the lead story on newscasts. The optics of the debate would flip, and the onus would be on the administration to explain how minting a coin isn't as absurd as it sounds and isn't a gimmick and really would work.
But it remains, as Krugman himself admitted, an accounting trick.
Josh Marshall of Talking Points Memo notes that no one outside the Beltway is paying attention to the details of the debate right now, and "you hear relatively serious people on the news acting as though it's Obama asking to spend more money or even unlimited money. So you have misunderstandings about what it means, compounded by tendentious misrepresentations and then simple inattention. But, as we're already seeing on the standard misinformation sites, the second you start talking about the president minting a special trillion dollar quarter, people pop up and say, 'What the F#*% are you talking about?' In other words, the platinum coin has the additional magic of making it look like the President is the one doing something reckless and totally crazy rather than Congressional Republicans who are the ones really doing it."
And then the GOP would just retrench even further. They certainly wouldn't given in that point.
Obama might still have the same problem, and politically, he'd have absolved the GOP of its responsibility, one that he has called on them to exercise since his election.
Now, this calculation might change if the House Republican conference really does decide to allow a government default. The administration might reverse its position at the last minute if it absolutely has to. Better a viable gimmick than a catastrophic default. But if it does wait until the last minute to resort to a coin trick, it will have done so because Republicans forced him to.