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On Sunday, Treasury Secretary Jack Lew said that Congress was "playing with fire," and warned the U.S. could default in just over a week.
"We continue to believe that the bigger risk event for markets remains a potential breach of the debt ceiling (around the 17 October) and expect such an event to be broadly risk negative," said Barclays analysts in a morning research note.
On Sunday, Republican House Speaker John Boehner warned he did not have a sufficient majority to pass legislation on raising the $16.7 trillion borrowing limit without spending cut conditions attached. Speaking to ABC television over the weekend, he added that the U.S. was on the path to a credit default.
However, the chief executive of credit rating agency Moody's Investors Service ruled out the prospect of a default, even if an agreement on the debt ceiling is not reached next month.
"It is unlikely that we go past October 17 and fail to raise the debt ceiling, but even if that does happen, then we think that the U.S. Treasury is still going to pay on those Treasury securities," Moody's CEO Raymond McDaniel told CNBC.
(Read more: Wall Street gets ready to trade defaulted US debt)
This week, the shutdown is likely to continue to disrupt the flow of official economic data, meaning third-quarter earnings may garner extra attention as a means of gauging the state of the recovery. On the economic front, consumer credit numbers will be reported by the Conference Board at 3 p.m. ET.
Alcoa declined after Morgan Stanley cut its rating on the aluminum producer to "equal weight" from "overweight." The former Dow component is slated to post earnings after the close Tuesday.
Apple ticked higher after Jefferies upgraded the tech giant's stock to "buy" from "hold." Separately, All ThingsD reports the SEC has ended an investigation into Apple's overseas cash and tax practices without taking any action.
BlackBerry jumped after Reuters reported Friday, that the troubled smartphone maker is talking to Cisco, Google and SAP about selling all or parts of the company, citing sources familiar with the matter In addition, Macquarie upgraded its rating on the company to "neutral" from "underperform."
Meanwhile, the dollar faces its fifth losing week, according to a CNBC poll of currency traders, analysts and strategists. Though some forecasters see declines of as much as 2 percent for the U.S. dollar index, which tracks the greenback against a basket of six major currencies, the selling may be contained as the market looks towards a resolution of the budget impasse.
—By CNBC's JeeYeon Park (Follow JeeYeon on Twitter: @JeeYeonParkCNBC)
On Tap This Week:
MONDAY: Consumer credit
TUESDAY: NFIB small biz optimism index, international trade*, Fed's Pianalto speaks, Fed's Plosser speaks, 3-yr note auction, Google announcement; Earnings from Alcoa, Yum Brands
WEDNESDAY: Mortgage applications, wholesale trade*, oil inventories, 10-yr note auction, FOMC minutes, Nike investor mtg; Earnings from Costco, Family Dollar, Chevron (interim report)
THURSDAY: Jobless claims, import/export prices*, Fed's Bullard speaks, natural gas inventories, 30-yr bond auction, Treasury budget*, Fed's Williams speaks, Fed balance sheet/money supply, chain-store sales, Draghi speech
FRIDAY: PPI*, retail sales*, consumer sentiment, business inventories*, Fed's Rosengren speaks, IMF annual mtg; Earnings from JPMorgan Chase, Wells Fargo
*Data will not be released due to the government shutdown.
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