"The comments by Boehner hinting at a willingness to broaden the tax base was a reasonable start that is probably helping to calm markets today," said Alan Ruskin, an analyst at Deutsche Bank.
An agreement is needed if the U.S. is to avoid the so-called fiscal cliff — a combination of higher taxes and government spending cuts that automatically take effect unless Congress agrees on a new budget by Jan. 1. Economists warn that a failure to reach a concrete decision will push the world's largest economy back into recession.
Moody's and Fitch have both warned that the U.S.'s triple A credit rating may come under threat if a deal isn't forthcoming. Last year, rival Standard & Poor's stripped the U.S. of its top-tier rating amid the political infighting in Washington.
"The hope is that politicians will be more inclined to be flexible given they don't have to worry about being re-elected for quite some time yet," said Michael Hewson, markets analyst at CMC Markets.
Despite worries over the fiscal cliff, the dollar garnered support on Wednesday through its perceived status as a haven at a time of financial distress. That remained, albeit modestly, Thursday, with the euro trading 0.1 percent lower at $1.2740.
Earlier in Asia, markets tumbled, tracked their counterparts in Europe and the U.S. the day before. Japan's Nikkei 225 index shed 1.5 percent to close at 8,837.15, while Hong Kong's Hang Seng sank 2.4 percent to 21,566.91.
In mainland China, the Shanghai Composite Index lost 1.6 percent to 2,071.51, while the Shenzhen Composite Index lost 2.3 percent to 831.71.
On Thursday, China's weeklong Communist Party congress began — the once-in-a-decade forum to name China's top leadership. Markets are looking for hints on how the new leadership plans to tackle the nation's economic slowdown.
In the oil markets, benchmark oil for December delivery was up 57 cents to $85.01 per barrel in electronic trading on the New York Mercantile Exchange. The contract fell $4.27 amid the turmoil on Wednesday.