With just weeks to go before the United States runs out of cash, the standoff has become the key topic on trading floors on fears that a US failure to pay its bills will send shockwaves through markets and the global economy.
Months of negotiations have failed to break the deadlock and lift the borrowing limit from the current $31.8 trillion, but things appear to be moving in the right direction after a series of Biden-McCarthy meetings.
After their latest get-together on Monday, the Republican Speaker said: "I felt we had a productive discussion. We don't have an agreement yet, but I did feel the discussion was productive in areas (where) we have differences of opinion."
He added that negotiators would "work through the night" to move the sides closer and that he and Biden would "talk every day to try to find a way to get this done".
For his part, Biden also described the talks as "productive" but that there were still "areas of disagreement".
While the two sides agree a default must be averted, they continue to disagree on certain issues. Democrats want to close tax loopholes to raise revenue and Republicans are calling for spending cuts.
Still, there is a broad view that a deal will eventually be done.
- Fed vs inflation -
"Right now, there's probably going to be continued posturing by both sides, but at the end of the day, it'll probably be resolved last minute," Burns McKinney, at NFJ Investment Group, told Bloomberg Television.
"What we expect in the near term is heightened volatility."
After a mixed start to the week on Wall Street, Asia opened higher but was unable to maintain momentum.
Tokyo, Hong Kong, Shanghai, Wellington, Manila and Bangkok fell, though Singapore, Seoul, Taipei, Mumbai and Jakarta edged up.
Paris and Frankfurt fell in the morning as data showed eurozone economic growth slowed in May. London was also lower.
The Fed was also in focus ahead of next month's policy meeting, with discussion revolving around whether it will lift rates again or stand pat for the first time since starting its hiking campaign more than a year ago.
St Louis Fed chief James Bullard said he saw another two increases before the year's end in order to tame inflation, which is still more than double the bank's two percent target.
"I think we're going to have to grind higher with the policy rate in order to put enough downward pressure on inflation and to return inflation to target in a timely manner," he said at a forum in Florida.
And Minneapolis Fed president Neel Kashkari told CNBC that while officials could pause next month, "what's important to me is not signalling that we're done".
"If we were to skip in June that does not mean we're done with our tightening cycle, it means to me we're getting more information," he said. "Do we then start raising again in July, potentially?"
- Key figures around 0810 GMT -
Tokyo - Nikkei 225: DOWN 0.4 percent at 30,957.77 (close)
Hong Kong - Hang Seng Index: DOWN 1.3 percent at 19,431.25 (close)
Shanghai - Composite: DOWN 1.5 percent at 3,246.24 (close)
London - FTSE 100: DOWN 0.1 percent at 7,760.16
Euro/dollar: DOWN at $1.0796 from $1.0815 on Monday
Pound/dollar: DOWN at $1.2400 from $1.2435
Dollar/yen: DOWN at 138.47 yen from 138.57 yen
Euro/pound: UP at 87.05 pence from 86.95 pence
West Texas Intermediate: DOWN 0.3 percent at $71.82 per barrel
Brent North Sea crude: DOWN 0.3 percent at $75.77 per barrel
New York - Dow: DOWN 0.4 percent at 33,286.58 (close)
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