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 Barack 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.
Chris Scicluna, an economist at Daiwa Capital, said that market expectations were for a deal to eventually be struck, to avoid a disorderly default.
"Any agreement is unlikely to be swift in the finalization — with a significant probability that it will come after Thursday's debt ceiling deadline has passed — and also still seems more likely to offer a temporary rather than lasting solution to the impasse," Scicluna said in a morning research note.
(Read more: As shutdown drags on, is more global easing coming?)
U.S bond markets will be closed for Columbus Day on Monday and banks will also be shut.
Facebook edged lower after the social-networking giant said it would acquire start-up app-maker Onavo. Financial terms of the were not immediately disclosed.
In Europe, a two-day meeting of euro zone finance ministers starts on Monday and will discuss, among other topics, Greece and banking supervision. Meanwhile, both Ireland and Italy are preparing for 2014 budget discussion on Tuesday.
(Read more: Ireland risks long-term pain for short-term gain)
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)