As I wrote before, simply not increasing the debt ceiling and forcing the government to reduce spending by 40% in a matter of days would be disastrous for the GOP politically, especially if it went on for longer than a few days or a week. The change would be too sudden and some Republican-friendly constituencies, like seniors, could be out of cash making them change their votes markedly in the 2014 elections. And we know for certain that the GOP would receive the vast majority of the blame if this were to happen (unlike with the fiscal cliff, only Republicans are really talking about not increasing the debt limit).
But then what happens if the Republicans vote against increasing the debt ceiling and Obama whips out a trillion dollar platinum coin? First, the government doesn't decrease spending and all the usual checks go out on time. Second, the Democrats will suddenly be blamed for using an obscure loophole to circumvent Congressional oversight of spending, the will of the people and the Federal Reserve. They will also be blamed for any uptick in prices (especially oil and food) as the coin would be viewed as increasing the money supply markedly (37% per trillion). And it's not like one coin will be enough. The last two trillion dollar debt ceiling increase lasted less than two years so they would have to probably mint coins regularly to keep there drunken sailor rate of spending up.
Sure, there is no guarantee that Obama will agree to mint a coin but it seems that pressure from many of his core constituencies and the media (but I repeat myself) will force him to do it.