Without an increase to the $16.7 trillion debt limit, the Treasury will lack the funds to pay its debts from late October/early November onward.
"We continue to expect no solution this week, and the ongoing government shutdown means that today's U.S. data will once again be postponed," said Chris Scicluna, an economist at Daiwa Capital.
(Read more: Six dangerous myths about the debt ceiling)
JCPenney spiked higher after the struggling department store chain posted a smaller decline in same-store sales for September, adding it sees positive signs in many areas of its business.
Talisman Energy soared after billionaire investor Carl Icahn Tweeted that he had purchased about 61 million shares of the oil producer and may seek a seat on the company's board.
Also, Nuance rose after Icahn said he had reached an agreement with the speech recognition software maker to seat two of his choices--one being his son Brett--to the company's board of directors.
In the absence of hard economic data due to the shutdown, investors will focus on the upcoming third-quarter earnings season.
Former Dow component Alcoa and KFC parent company Yum Brands are slated to post quarterly results after the market close tonight.
In addition, several Federal Reserve officials are scheduled to speak throughout the day. Sandra Pianalto and Charles Plosser are expected to speak at 12:30 pm ET. In addition, the Treasury is scheduled to auction $30 billion in 3-year notes on Tuesday.
Asian shares pared most of their early losses on Tuesday, as mainland Chinese and Hong Kong markets climbed in the first day of trade after the "Golden Week" public holiday.
(Track Asian markets here)
"We have had better Chinese data released over the week, as well as reports of a bumper retail sales and domestic tourism during the 'Golden Week'. Hence, the shorter-term effect may see domestic demand lending support to Chinese indexes, until reality of a [potential] U.S. default sinks in," said Desmond Chua, market analyst at CMC Markets, in a research note.
Shares were lower in Europe meanwhile, with U.K. retailers trading down after the British Retail Consortium reported weaker sales growth. But technology stocks were higher, boosted by a bounce in shares of French company Alcatel-Lucent, which announced the latest part of its cost-cutting plan.