Over the weekend, there were plenty of trader commentary passed around noting that during the last shutdown, in 1995-1996, the market was shut twice for a period of about three weeks. During the first shutdown, from November 13th to November 19th, the S&P 500 was up about 1.2 percent. During the second shutdown, from December 15th to January 6th, the market initially fell, but ended essentially unchanged.
Markets seem to believe that the same thing will happen. While the S&P 500 may be down 15 points, volume is still light.
I said last week that I think the markets are underestimating that the fight over the budget could merge with the fight over the debt ceiling --and become one giant mess. The markets are not pricing in any prolonged conflict, and that is dangerous.
While the Fed and the FDIC would remain open, as would Fannie Mae and Freddie Mac (both are private agencies, technically) other government agencies involved in financial matters may not be.
It's not clear how long the SEC would remain open-- some "essential" functions like monitoring of markets would certainly continue. But IPO reviews would almost certainly cease, as would most enforcement actions. The SEC's plan for a shutdown is here.
Large parts of the CFTC may also shut down. The CFTC has said only about four percent of its employees were essential, so while market surveillance will continue, it will likely be curtailed and any work on policy issues would come to a halt.