The thing is that a lot of investment vehicles have regulations saying that they must only invest in AAA investments. (from back in the days when Rating Agencies weren't a rubber stamp collusion with Wall Street). They have already said they will downgrade USA if it technically defaults.
This means that when midnight hits, all those funds will immediately start selling their 'solid' US Bond investments and that will trigger other computer programs that work on algorithms and so a sell-off will occur. Inside that noise, nervous bond holders like China will start dumping and so it goes.
The alternative is that Obama will risk impeachment by acting unilaterally and that would mean business as usual for Wall street, and the rest of the world, and political death for Obama.
The big danger is that a big player will say 'I'm not risking default' and sell. It could be one hedge fund, one country, or even a popular swell of housewife investors in Japan. That would then trigger the algorithms. That is the wild card the pollies are playing with.
Some of the Republicans elected on the 'no more debt/small government' platform , could easily hold fast against Obama - some of them oppose the teaching of Evolution so a little matter like international finance to keep their constituents happy won't be an issue.
They will raise the debt ceiling - they always have done - but the wild cards are those algorithms and the unpredictability of human behaviour. That is why this 'arrogance of Rome' is so dangerous.