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Adding to the gloom, data showed China's export growth unexpectedly fizzled in September, underscoring worries about flagging global demand, and annual consumer inflation quickened to a seven-month high.
MSCI's broadest index of Asia-Pacific shares outside Japan, which had hit a three-week high on Friday on hopes a US deal was imminent, dropped 0.3% and China's CSI300 index slipped 0.2%.
Markets in Japan and Hong Kong are closed on Monday for public holidays.
US stocks had risen strongly ahead of the weekend on hopes a deal to raise the $16.7 trillion federal borrowing limit was near. However, politicians remain at loggerheads as the October 17 deadline approaches and US stock index futures fell 0.7% in Asian trade.
US equity markets will trade on Monday, although some markets, such as the Treasury market, will be shut for the Columbus Day holiday. In Asia, US Treasury futures edged up 4 ticks.
Failure to break the stalemate before Thursday's deadline would leave the world's biggest economy unable to pay its bills in the coming weeks, an outcome that is unthinkable for the global economy and financial markets. IMF chief Christine Lagarde warned of "massive disruption."
Still, trading has remained relatively calm as many analysts expect Republicans and Democrats to strike a last-minute deal, believing US politicians would want to avoid the dire consequences of a default.
"Most likely, a solution will be found before, or be in the making, by October 17," analysts at Nomura wrote in a client note.
"The tail risk comes into play if there is no clear framework for a solution by October 17. Entering this tail would see risk jump in terms of funding market stress and risk assets more broadly."
Some financial institutions have reduced the use of Treasury bills as collateral for trades as the deadline gets closer. Hong Kong's securities exchange is applying a bigger discount on US Treasuries used as margin collateral.
UNCERTAINTY AHEAD
The failure of the weekend talks in Washington saw investors react by seeking safety in the yen.
The dollar fell 0.3% to 98.285 yen and the euro dipped 0.1% to 133.30 yen. The Australian dollar eased 0.1% to 92.81 yen.
The dollar index, which tracks the greenback against a basket of major currencies, was a touch softer.
In commodity markets, gold fell 0.2% to just below $1,270 an ounce, adding to last week's 2.9% decline.
Brent crude dipped 0.2% to around $111 a barrel on concerns that the US debt standoff and slower growth in China would crimp demand.
"China still faces significant external headwinds while a recovery in domestic demand is lifting import growth," HSBC said in a note on the weak export data.
"Beijing should keep its accommodative policy and steer structural reforms to sustain a recovery driven by domestic demand," it added.
