Stocks ended higher after a negative morning on Monday, as investors were encouraged by signs of progress in a budget deal in Washington.
Stocks responded positively to word of a meeting between President Obama and Congressional leaders. It was promptly postponed to allow leaders in the Senate "time to continue making progress" towards a solution that raises the debt limit and reopens the government, according to a statement from the White House.
The Dow Jones Industrial Average, which dropped nearly 100 points in the morning, made modest gains in the afternoon to close 64 points ahead. Pfizer and Boeing led the gainers, while Merck declined.
The S&P 500 and the Nasdaq were also in positive territory after slipping early on. The CBOE Volatility Index (VIX), widely considered the best gauge of fear in the market, jumped above 17.
The Russell 2000 small cap index rallied to briefly hit a fresh high.
Among key S&P sectors, techs and energy led the gainers, while utilities sagged.
Major averages rallied last week amid hopes for a deal in Washington. The Dow and S&P closed in the black for the week and all three indexes logged their second-best gains for the year on Thursday.
"Today with a semi-holiday (Columbus Day), it will be a game of cat and mouse—the U.S. bond market's closed, Canada's closed, Japan's closed…so the markets will be extremely thin and vulnerable," said Art Cashin, director of floor operations at UBS Financial Services, noting that equities on Columbus Day have a 65 to 70 percent bias to the upside.
The U.S. government needs to raise the debt ceiling by Thursday in order to avoid a potential default on its debt — the Treasury needs to make a Social Security payment of around $24 billion on Nov. 1.
Stocks initially opened lower after weekend talks between lawmakers to strike a deal were unsuccessful, although there were signs of improvement on Sunday, when Senate Democratic leader Harry Reid said he had a "substantive"and "productive conversation" with Senate Republican leader Mitch McConnell. This followed President Obama's Friday rejection of a proposal by House Republicans for a short-term increase of the ceiling until November 22.
(Read more:Senate leaders talk; GOP blames Obama for gridlock)
As global concerns over the possibility of a default grew, the chief of the International Monetary Fund, Christine Lagarde, said the situation was "very, very concerning" and warned that "creative accounting" was not the right solution.
The shutdown has furloughed nearly 350,000 federal workers, impeded various government services, put continued operations of the federal courts in doubt and stopped the IRS from processing tax refunds.
(Read more: As shutdown drags on, is more global easing coming?)
Several major companies are slated to post earnings results this week including Citigroup, Coca-Cola, Bank of America, IBM, Goldman Sachs, GE and Morgan Stanley. (See below for full earnings calendar)
S&P 500 companies are expected to post earnings growth of 4.2 percent in the quarter, down from the 8.5 percent rate that had been forecast on July 1, according to the latest data from Thomson Reuters data. Of the 31 S&P components that have reported so far, about 55 percent have topped expectations, below the historical average of 63 percent.
Japan and Hong Kong were shut for public holidays in Asia. China's Shanghai Composite extended last week's 2.5 percent gain, on the news that annual consumer inflation rose to a seven-month high in September. However, gains were pared by weekend data that showed a surprise 0.3 percent drop in exports in the same month.
(Read more: Why Chinese actually envy the US shutdown)