While markets expect U.S. politicians will eventually strike a deal, they are getting nervous as the deadline nears without any tangible progress between Democrats and Republicans.
MSCI's broadest index of Asia-Pacific shares outside Japan dipped 0.3 percent while Japan's Nikkei average erased earlier losses but held near a five-week low.
"Everyone had been thinking that U.S. politicians will become grown-ups in the end. But some people are starting to think they look too childish to become grown-ups in time," said Tohru Yamamoto, chief fixed income strategist at Daiwa Securities.
President Barack Obama said he would be willing to negotiate only after Republicans agree to re-open the government and raise the debt limit with no conditions. Republican House Speaker John Boehner said he was disappointed by the president's approach.
"At the moment there is no sign of compromise, although the market expects Republicans will eventually agree to raising the debt ceiling," said a proprietary trader at a Japanese bank.
Wall Street shares dropped to one-month low on Tuesday, with S&P 500 index .SP500 falling 1.2 percent. The CBOE Volatility Index .VIX, a measure of investor anxiety, rose also nearly 5 percent to close at its highest since June 20.
The budget impasse overshadowed news Obama will nominate Federal Reserve Vice Chairwoman Janet Yellen as the next head of the U.S. central bank.
U.S. stock futures gained about 0.3 percent as Yellen is seen as a proponent of dovish policy. The government shutdown is already disrupting U.S. data flows, helping to put talk of tapering in the Fed's stimulus completely off the table for now.
Some investors are starting to take precautions to protect against the possibility of a U.S. default by shunning U.S. debt maturing in late October and early November.
The yield on four-week U.S. government bills hit a 5-year high above 0.3 percent of on Tuesday.
Against a basket of major currencies, the dollar was at 80.04, close to an eight-month low hit last week.
Ironically, the dollar found some support from the fiscal standoff, as foreign banks bought the U.S. currency just in case a deal is not reached and liquidity dries up.
The dollar rose to 97.21 yen after having hit a two-month low of 96.55 yen on Tuesday. The euro traded at $1.3568, below an eight-month peak of $1.36465 hit last week.