No one can predict the future. If I could I wouldn’t be teaching but instead making lots of money trading stocks. That said, my best guess is that the shutdown cannot last more than 3 weeks but likely will last 11 days.
Why 11 days? Because while the shutdown occurs all federal paychecks are not being processed. The next federal pay day is October 11th. To see when Federal employees get paid look at this link.
Many of the people who work as air traffic controllers, federal prison guards, airport screeners, FBI, CIA, etc. get paid every 2 weeks by direct deposit (also called EFT – Electronic Funds Transfer). If these people don’t get paid on the 11th, many will call in sick and key functions will grind to a halt.
No politician wants to be seen as the man/woman who allowed federal prisoners to riot, planes to crash or terrorists to plot an attack because they were grandstanding on TV about health care reform, which is why I believe the shutdown has to finish around October 11th.