First, let me talk about the obvious things. A one trillion dollar platinum coin is not composed of one trillion dollars worth of platinum.
Similarly, a one hundred dollar bill is not made out of one hundred dollars worth of paper. Or make that cotton, as US 'paper' currency is actually made out of cotton (plus some plastics and other synthetics). It's called a one trillion dollar simply because that's what we engrave on it and claim it's worth.
Why a platinum coin - as opposed to say a gold one, or even a cotton/paper bill? Because congress has put in rules and regulations affecting how much paper currency we can print and also how much gold, silver, and other coins we can mint. But they put in a loophole to let Federal government mint any amount of platinum coins they want.
They did this to support coin collectors - both the sane ones doing it as a hobby with minor investment potential and the insane 'PUT YOUR MONEY IN GOLD AND PRECIOUS METAL! THE WORLD IS ENDING!!! NOW!" Glen Beck people.
Done with the basics, now let's talk about the results of doing this.
Lots of it.
That's why congress put limitations on printing currency in the first place.
Is it an option? Yes. It is even a legal one. Would I personally recommend it? YES. Will the president do it? He said no.
America has had a huge period of low inflation. For the past 70 or so years we avoided deflation entirely, but for the past 30 years we have had almost no inflation. This is in fact one of the reasons why we had the housing problem. If we had had some nice standard 10% inflation in 2005, 2006, and 2007, then houses would have gone up in value. They could have sold most houses for more than their worth and the housing crisis would not have happened.
More importantly, inflation has been relatively low (see chart below) since the 1980's. Our economy could definitely deal with a short period of inflation. It might even be good for it. Yes, some people are hurt by inflation (all those on a fixed income or who have most of their money tied up with long term fixed low rate securities). But at the same time, many would benefit - for example those who have long term fixed rate debt (i.e. 30 year fixed rate mortgages). Full disclosure - I have a 30 year fixed rate mortgage.
Is it going to happen?
Obama announced he won't. A foolish move on his part - he should have used it as a threat to get the GOP will cave.
Why? Because the GOP loves the wealthy and the wealthy have a lot of their money tied up in the long term fixed rate securities. They also don't want to piss off the elderly, as they have already screwed up with failed attempts to 'fix' social security.
So Obama should have threatened the GOP and they would have caved. Because it is exactly the kind of threat the GOP would like to use against the DNC. Which also makes it is exactly the kind of threat they would bow down to.