In the U.S., the Dow Jones industrial average was up 0.7 percent at 13,223.70 while the broader S&P 500 index rose 1 percent to 1,427.22.
Though the budget measures associated with the "fiscal cliff" would not all be introduced at once and the Republicans have indicated a willingness to increase taxes on households earning over $1 million, investors won't breathe easily until a deal is signed, sealed and delivered.
"Investors have so far remained hopeful that an agreement can be reached in a sufficiently timely manner," said Nick Bennenbroek, an analyst at Wells Fargo Bank. "However, with a year-end deadline for a deal now looming closer, those budget developments should become increasingly important through the end of December."
In recent weeks, the dollar had suffered, at least against the euro, due to the U.S. budget fears. On Monday, the currencies were steady, with the euro up 0.1 percent at $1.3171.Elsewhere in Asia, China's shares fared fairly well as its new leaders promised more spending if needed to underpin a wobbly economic recovery. Those hopes helped the Shanghai Composite to rise 0.4 percent to 2,160.34 and the smaller Shenzhen Composite index to end 0.4 percent higher to 819.58. On Sunday, China's new Communist Party leaders under party General Secretary Xi Jinping pledged a "proactive fiscal policy" and "prudent monetary policy" in a statement carried by the official Xinhua News Agency. They were references to the willingness to boost spending if needed and keep credit easy so long as inflation stays low. Elsewhere in Asia, South Korea's Kospi lost 0.6 percent to 1,983.07 and Hong Kong's Hang Seng was down 0.4 percent at 22,513.61. In commodity markets, the price of benchmark crude oil in New York was up 79 cents at $87.52 a barrel.