Markets had underestimated the ability of Washington to end up at an impasse. Many analysts and traders had thought politicians would keep the government from shutting down, but now they are becoming concerned that it will not be a quick shutdown because the spending resolution will become part of a bigger battle over the debt ceiling.
There is also growing concern that there will be no compromise on the debt ceiling, and President Obama may then raise it without Congressional support to avoid a default, triggering lawsuits.
Serebriakov said it's not clear what would happen if the U.S. reached the debt limit. He said it could trigger a flight-to-safety reaction, just as the Standard and Poor's downgrade of the U.S. AAA credit rating did two years ago.
(Read more: Get out the rally hats: Shutdowns are bullish!)
Chandler said the dollar, however, is sending an important message, and that is that investors do not expect a worst case scenario. It would be much weaker if investors really believed the U.S. could hit the debt ceiling or that Congress would allow a default to occur.
But until the situation is resolved, "It stays on edge. It keeps some players on the sidelines, it affects liquidity and it's nervous, which means there could be sharp moves on nothing. This is short-term noise," Chandler said.
Besides the weaker dollar Wednesday, stocks were on edge, after ignoring the shutdown Tuesday. The Dow was off 58 at 15,133 and the S&P 500 was off 13 at 1693.
Chandler said the shutdown makes it less likely the Fed will pare back its $85 billion bond purchase program this year. That also could be weighing on the dollar, since quantitative easing is a negative for the dollar.
Traders had been hoping the monthly jobs data, an important metric for the Fed would send a signal as to whether the Fed would move toward tapering at its Oct. 30 meeting. Instead, the data is likely to be delayed and they will instead focus on the economic reports that are available. The government will continue to issue weekly jobless claims data.
Claims are released at 8:30 a.m. ET Thursday, and there will also be the Institute of Supply Management's non-manufacturing survey at 10 a.m. .
—By CNBC's Patti Domm. Follow her on Twitter