Hong Kong's Hang Seng, trading for a half-day, closed marginally lower at 22,656.92. Benchmarks in New Zealand, Singapore and India also declined.
Mainland Chinese stocks rose after a private survey showed the country's manufacturing growth at its strongest level in 18 months in December. The Shanghai Composite Index jumped 1.6 percent to 2,269.13 and the smaller Shenzhen Composite Index added 0.9 percent to 881.17.
Markets in Japan, South Korea, Thailand, the Philippines, Indonesia and Taiwan were closed for the New Year's holidays. In early trading in Europe, Britain's FTSE 100 was 0.3 percent lower to 5,905.71. France's CAC-40 was 0.1 percent lower at 3,615.28.
Even if Washington bypasses the fiscal cliff, the next crisis is just around the corner, in late February or early March, when the government reaches a $16.4 trillion ceiling on the amount of money it can borrow.
Republicans won't go along with raising the limit on government borrowing unless the increase is matched by spending cuts to help attack the long-term debt problem. Failing to raise the debt ceiling could lead to a first-ever U.S. default that would roil the financial markets and shake worldwide confidence in the United States.
Compounding that is U.S. earnings season in February, Esho said.
"There are some very aggressive assumptions for earnings to improve in 2013 and ... if the earnings numbers don't meet expectations, it is going to be quite disappointing," Esho said.
Benchmark oil for February delivery rose 8 cents to $90.91 per barrel in electronic trading on the New York Mercantile Exchange. The contract fell 7 cents to finish at $90.80 per barrel in New York on Friday.
In currencies, the euro fell to $1.3186 from $1.3221 late Friday in New York. The dollar was unchanged at 86.07 yen.
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