It is funny that some people are asking where the U.S. government would get all that platinum, when in fact all it would take is enough to mint a coin and inscribe $1,000,000,000,000 on it. Of course, as Barro notes, this notional coin is not a "platinum standard," but I think it does highlight a difficulty that any commodity standard does face: the equation of x amount of a commodity to y amount of dollars ultimately rests on a monetary issuer's assertion that it will uphold that value--exchanging between cash and metal on demand and not, say, deciding tomorrow that the new rate is x = 2y, or x = 2 trillion y.
As such, metal-backed money is not fundamentally different from fiat money. There's no easy way for policymakers to tie their own hands, in monetary policy or in fiscal policy (see, e.g., "debt ceiling"). At least, though, an unanticipated benefit if the U.S. government does mint a trillion-dollar coin would be to underscore the absurdity of seeking "sound money" based on a supposedly solid link to any metal.
UPDATE 1/9 2:43PM: A piece at Business Insider takes the opposite view--arguing that resistance to the platinum coin idea shows that people are stuck in a gold-standard mentality. According to the writer, there actually are no problems involved in the government vastly expanding the money supply, just print away or mint a coin with an arbitrary amount or whatever. I think that might work on a different planet, one where there's no worry that, say, foreign bond investors will ever stop buying a government's debt.
Also, Megan McArdle has a well-justified rant about not just the platinum coin but the deeper dysfunction it represents. Excerpt:
Try this exercise: name some of President Obama’s campaign pledges. Unless you were actually covering the elecetion, I bet you can only name one: the pledge to raise taxes on people who made more than $250,000. No new programs to solve some problem, no high-concept bargain to unite the nation . . . no, the one thing that Democrats wanted to do was raise taxes for 2% of taxpayers, and only 2% of taxpayers. Not to pay for anything in particular, but just because the rich had too much. And why was this—rather than some actual policy program—the centerpiece of his agenda? Because his base liked it, and because opposing it made the ultra-rich Mitt Romney look like a selfish heel.Me: The debate I wanted to see.