After weeks of wrangling, the two announced that an agreement had finally been reached and urged lawmakers on both sides of the aisle to vote for it before the government runs out of cash on June 5.
However, there is some nervousness on trading floors as the bill contains plenty of elements that are likely to anger Democrats and Republicans alike.
For now, dealers are upbeat as the breakthrough lifts the threat of a debt default by the United States that economists warn could hammer the global economy and cause market turmoil.
The bill will suspend the debt ceiling until January 1, 2025 and place curbs on federal spending that will please some Republicans, but it does not deliver the big cuts right-wingers wanted and progressive Democrats would have balked at.
"The agreement prevents the worst possible crisis," Biden said at the White House on Sunday. "Which means no one got everything they want."
"But that's the responsibility of governing. I strongly urge both chambers to pass that agreement."
He added: "It takes the threat of a catastrophic default off the table, protects our hard-earned and historic economic recovery and... represents a compromise that means no one got everything they want."
And McCarthy said: "We know anytime we sit and negotiate with two parties, that you got to work with both sides of the aisle. So it's not 100 percent of what everybody wants."
Hopes that a deal was in the works lifted all three main indexes on Wall Street on Friday, and Asia picked up the baton Monday.
Tokyo rallied more than one percent as did Sydney, while Hong Kong, Shanghai, Singapore, Taipei, Manila and Wellington were also in the green.
- Fresh pressure on the Fed -
"The obvious positive interpretation is that a negative tail risk is close to being taken off the table," Dan Suzuki, of Richard Bernstein Advisors, said.
"With the distraction of the debt ceiling fading into the background, investors can now refocus their attention on the underlying fundamentals. One concern, though, is that the fundamental picture remains precarious."
However, in a sign of the opposition the bill will face, Republican Representative Dan Bishop -- a member of the ultra-conservative House Freedom Caucus -- tweeted a vomit emoji and said McCarthy secured "almost zippo".
Nicholas Creel, a political analyst and business law professor at Georgia College and State University said: "Overall, the deal is probably best viewed as a win for Biden and Democrats given that it contains fairly modest spending cuts and would prevent another debt ceiling showdown or a government shutdown during the remainder of Biden's presidency.
"Nobody has enough power to get too much of what they want right now, so a compromise like this that makes everyone a little unhappy is probably the best anyone could have hoped for."
Observers said investors could now turn their focus back to the economic outlook, though data on Friday gave them further cause for concern.
The US Federal Reserve's preferred measure of inflation -- the personal consumption expenditures (PCE) index -- rose 4.4 percent year-on-year in April, up from 4.2 percent a month earlier.
The core index, excluding volatile food and energy prices, also rose, as did personal income and spending.
The figures will put fresh pressure on the central bank to continue lifting interest rates to bring inflation under control and deal a blow to hopes it will pause next month after more than a year of hikes.
- Key figures around 0230 GMT -
Tokyo - Nikkei 225: UP 1.3 percent at 31,325.84 (break)
Hong Kong - Hang Seng Index: UP 0.1 percent at 18,764.409
Shanghai - Composite: UP 0.3 percent at 3,223.43
Pound/dollar: UP at $1.2356 from $1.2350 on Friday
Euro/dollar: UP at $1.0733 from $1.0725
Dollar/yen: DOWN at 140.49 yen from 140.59 yen
Euro/pound: UP at 86.88 pence from 86.84 pence
West Texas Intermediate: UP 1.1 percent at $73.49 per barrel
Brent North Sea crude: UP 1.0 percent at $77.75 per barrel
New York - Dow: UP 1.0 percent at 33,093.34 (close)
London - FTSE 100: UP 0.7 percent at 7,627.20 (close)
dan/qan
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