I thought I had written about the platinum coin last time around, but if I did, I can't find it. But basically, I think we all covered this last time around...
At some point, Barack Obama will, if Congress does not act, be faced with an impossible choice. He will have clear, conflicting imperatives. Congress will have obligated him to spend money; not spending money that Congress has appropriated is an impeachable offense. The government will also be obligated to make good payments on current debts; he's clearly required to do that, as well. However he also will will be without money to do those things, not have the authority to borrow any more, thanks to the debt limit.
So he will have to choose to have the government violate one of those legally binding commitments.
One option is to blow past the debt limit. He could do so by following an interpretation of the 14th Amendment which essentially makes the debt limit unconstitutional; he's sworn that off, but he could always retreat back to it anyway. He could mint the coin. Kevin Drum has been campaigning against it and believes it's obviously not legal, but Jack Balkin disagreed during the last debt limit run-up and said it was perfectly kosher...I'm not a lawyer, but I think Drum is wrong that it's a slam-dunk against it. Moving on: he can declare that Congress has given him conflicting mandates, and since he's forced to choose he'll keep spending by borrowing. Or he can come up with some other inherent executive power that allows him to keep the government operating normally.
None of these are good choices; the debt limit is bad law, and it's massively irresponsible for House Republicans to hold the economy and the financial standing of the nation hostage by using it. But there's a strong case, given the various bad choices, for blowing through the debt limit one way or another; the best choice would presumably be one that otherwise leaves the presidency and Congress unaffected.
That's if Congress doesn't act. What about before that? The White House is maintaining that they will "not bargain" over the debt limit, which is a sort of tough-sounding nonentity of a position...unless they are prepared to take it all the way. Which only makes sense if they're certain that House Republicans would cave and pass a clean debt limit increase, or if the president is prepared to blast through the debt limit in the even that there's no increase. In which case you get into all sorts of questions about best negotiation tactics. Should the White House announce, publicly, that it intends to blast through it? Do they just say it privately in negotiations? Keep it secret? The answer to that is going to depend on the bargaining situation and what they think the other side will do -- and the answer to which method of going through the debt limit is best may depend on how how they intend to use it before the deadline. If the president intends, for example, for House Republicans to absolutely believe he'll do it, then the face-silliness of the coin might detract from that; on the other hand, if they think Republicans will fold but want a back-up plan just in case, then they don't need an option which makes the most believable threat.