If the past is any indicator in the outcome of all this they will most certainly come to a last minute deal.
It's imperative to both sides wallets and political interests they don't let the Federal Government shut down for one second.
The press will report the tension and how Obama was so angry he had little white balls of spit in the corners of his mouth or something of human interest, but "by a miracle" both sides came to an agreement at the last minute.
This agreement will, in all likelihood, not be in the best interests of the American people, but this little show we're being forced to watch is interesting is it not? In the end this may well be a perfect ballet of more money for war, less for social services, higher taxes on the poor and middle class.
The rich remain unscathed.
Sure I may be wrong, however that's the way I see this panning out.