One, Obama will not negotiate.
There is a perfectly good reason for this. If Republicans can pass any legislation they want by shutting down government, they essentially run the whole government even though they have only one of three pieces traditionally needed for passing legislation. (The House can't pass legislation without the White House and Senate.) Republicans will have proven that they can dictate anything - even something as distasteful as dismantling Obama's signature legislation. It would be like asking FDR to give up the new deal or asking Reagan to give up on cutting taxes. Romney campaigned on exactly this (repealing Obamacare) and lost. To let House Republicans stop Obamacare would be the same as telling the American people that it doesn't matter if they voted for a Democratic Senate and President; the Republican agenda is what they'll get.
If Obama negotiates he doesn't just turn over his agenda to the Republicans who have now turned their agenda over to the Tea Party. He would essentially be telling the American people that majorities no longer matter; the 18% of Congressional districts who voted Tea Party are now calling the shots, the rest of the country be damned.
Because of this, Obama is not bluffing. He won't negotiate.
Two, the Republicans won't negotiate.
There is a perfectly good reason for this. Republicans believe government spending is bad for the economy. Shutting down government - in their minds - is a good thing, something that will liberate the economy like an Ayn Rand character freed from social obligations. Even the thought of not raising the debt limit sounds to them like a good idea. It's not that they don't care about the economy, it's that they don't understand how it works. The lesson they learned from the last debt ceiling negotiations was that we have too much debt, not that the threat of not paying their bills will make the stock market and larger economy stumble, perhaps even fall.
Rand Paul was named after a woman who proved her economic philosophy through novels. The Tea Party has no interest in an empirical method that suggests that abrupt changes in government spending could hurt the economy or that carbon emissions might cause climate change or that the earth actually circles the sun. They have beliefs and don't want them challenged. It's not even obvious that these social conservatives are any more interested in the economic progress that challenges their beliefs and traditions than are Afghan tribal leaders. Plus, economic catastrophe would prove that they were right about the dangers of debt.
The Republicans won't negotiate. They don't see any reason to fund government or pay their bills. You would think that with a 70% disapproval rate, they would care about re-election but they only run in their districts. While the rest of the nation is outraged, their constituents are cheering them on.
I've read that the Republicans are so intent on drowning the captain that they'll sink the ship. I don't think they're that malicious. I just think that they've been on a ship for so long they have no idea what it means to be in water. The Tea Party is not evil, they're just clueless. To segue into another metaphor, right now, the nation is trying to talk a toddler into giving up the handgun its pointing around the room. The toddler has no idea what the gun could do and anyone who comes close is in danger.
Someone is getting shot. That seems certain. We can only hope that won't be a bloodbath before it's over.