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Asian stocks were expected to open higher, with Japan's Nikkei index futures up 0.8%, after US Standard & Poor's 500 index reversed early losses to close up 0.4%, spurred by hopes of a US budget deal.
Many markets in the region, including Singapore, Indonesia, were closed for holidays.
US Senate Majority Leader Harry Reid said he and his Republican counterpart, Mitch McConnell, have made strong progress toward reaching a deal to end a partial government shutdown and lift the debt ceiling, averting a possible default, an outcome that is unthinkable for the global economy.
US S&P 500 E-mini futures added 0.1% in early Asian trade on Tuesday, though US Treasury futures slipped 5-1/2 ticks.
The dollar held steady at 98.67 yen, recovering from a low of 98.05 hit in the previous session. The greenback also stabilised at $1.35555 to the euro after slipping 0.1% on Monday.
"Risk sentiment remains resilient despite the lack of a clear breakthrough in the US debt ceiling and government shutdown negotiations," analysts at BNP Paribas wrote in a note.
"The Japanese yen's initial rally has now fully reversed although in the absence of an agreement the near-term risks are for a stronger yen," they added.
The plan under US Senate discussion would raise the $16.7 trillion debt ceiling by enough to cover the country's borrowing needs at least through mid-February 2014, according to a source familiar with the negotiations. It would also fund the government operations through the middle of January.
But any deal would have to win approval in the House of Representatives, where conservative Republicans have insisted that any continued government funding must include measures to undercut President Barack Obama's healthcare programme - non-negotiable for Democrats.
JPMorgan analysts said market reaction to the US budget impasse has been muted so far, though it did not believe investors were complacent.
"Our sense is not complacency, but more a belief that a true default, beyond a technical delay in payments lasting several days, is highly unlikely, and a lack of clarity of what such a default would mean for markets beyond a sense that it will be bad," they wrote in a note.
"Market participants appear to be preparing for the event risk of a delayed payment of US Treasury coupons and principals by adding liquidity and avoiding securities maturing around the debt ceiling deadline."
In the commodity markets, US crude slipped 0.2% to around $102 a barrel, giving up some of Monday's gains as traders bought contracts to cover short positions ahead of a possible deal in Washington.
