At a press conference on Tuesday, President Obama said he had yet to see serious proposals from the Republicans that would allow both sides to resolve their core differences to end the shutdown.
Among earnings, Costco declined after the warehouse club operator reported a weaker-than-expected gain in quarterly earnings as operating cost gained. Rival Wal-Mart also ticked lower following the report.
Family Dollar posted earnings that edged past expectations, but shares slumped after the discount retailer said it was taking a cautious approach to 2014. And same-store sales were flat in the fourth quarter, missing the company's July forecast for an increase of about 2 percent. Rivals Dollar Tree and Dollar General also ticked lower.
Chevron is scheduled to post its interim earnings report after the market close.
Third-quarter earnings are expected to grow 4.3 percent, while revenue is estimated to gain by 3 percent, according to the latest data from Thomson Reuters.
Men's Wearhouse spiked higher after the clothing retailer rejected rival Jos. A. Bank's unsolicited $2.3 billion takeover bid, saying the offer "significantly undervalues" the company.
U.S government debt prices moved higher on Wednesday with the yield on 10-year benchmark Treasury notes at 2.6255 percent on Wednesday, after closing at 2.638 on Tuesday.
The latest test of investor sentiment regarding the U.S. impasse will come on Wednesday as the Treasury plans to sell $21 billion in 10-year notes, ahead of a sale of $13 billion of 30-year bonds on Thursday.
On the economic front, mortgage applications climbed last week as demand for refinancing outpaced purchases, according to the Mortgage Bankers Association.
Wholesale trade data will not be released on Wednesday, as scheduled, due to the government shutdown.
Meanwhile, the minutes of the Fed's Sept. 16-17 meeting will be released at 2pm ET. Fed reports are not impacted by the government shutdown.
While Asian markets rallied on the news of the Yellen appointment, it wasn't enough to raise investor spirits in Europe. Stocks in the region traded lower, weighed down by rising concerns over a U.S. credit default with only nine days left for Congress to raise the debt limit before October 17.