MSCI's broadest index of Asia-Pacific shares outside Japan edged down 0.1% in early trade. It is headed for a monthly drop of 3.3%, the largest fall since March.
Japan's Nikkei was down 0.2% and Australia's ASX 200 fell 1.3%, while markets in Seoul rose 0.8%.
Futures pointed to small opening gains in China and Hong Kong. S&P 500 futures were steady, last trading 0.1% firmer, with moves slight ahead of the debate.
Also on the horizon is factory activity data from China, due at 0100 GMT, where a small pickup is expected as the world's second biggest economy extends its steady recovery from the coronavirus crisis.
A surprise could swing markets' mood.
"The sorts of numbers that would confirm China's recovery, from being 'first in to first out' of the pandemic, is proceeding apace," said Ray Attrill, head of FX strategy at National Australia Bank in Sydney.
Steady Asian trade followed a dip on Wall Street which snapped a three-day rally as traders approached the debate with trepidation and fretted about whether the next round of U.S. fiscal stimulus might be falling by the wayside.
The Dow .DJI and S&P 500 .SPX fell half a percent and the Nasdaq Composite dropped 0.3%.
In currency markets, the U.S. dollar was also down slightly before the debate, hitting one-week lows against the euro and Swiss franc. The dollar index fell 0.3%.
U.S. House Speaker Nancy Pelosi said on Tuesday she hoped to have a coronavirus aid deal with the White House this week, after speaking with Treasury Secretary Steve Mnuchin and making plans for further talks on Wednesday.
However White House economic adviser Larry Kudlow told CNBC that the Democrats' $2.2 trillion compromise relief bill still seemed too large - leaving plenty of room for the impasse to persist.
The economic impact of the coronavirus pandemic was underlined later Tuesday, when Disney DIS.N announced plans to lay off roughly 28,000 U.S. employees from its theme parks division.
One optimistic sign came on Tuesday when U.S. consumer confidence saw its biggest rebound in 17 years.
Investors will also be looking at Wednesday's ADP National Employment report, a precursor to official U.S. employment figures out Friday for the latest reading on the labour market.
Spot gold steadied at $1,895 an ounce.
Oil prices nursed losses amid caution ahead of the debate and rising coronavirus cases. U.S. crude CLc1 fell 1% to $38.92 per barrel and Brent settled at $41.03.
(Reporting by Pete Schroeder in Washington and Tom Westbrook in Singapore Editing by Shri Navaratnam) ((firstname.lastname@example.org; +65 6318 4876;))
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