Jensen Huang, the 60-year-old cofounder of chipmaker Nvidia. AFP
All three major indices were in positive territory, while Nvidia jumped more than seven percent on bullish sentiment over its role in artificial intelligence breakthrough technology.
About 20 minutes into trading, the Dow Jones Industrial Average was down 0.2 percent at 33,021.07.
The broad-based S&P 500 climbed 0.4 percent to 4,223.64, while the tech-rich Nasdaq Composite Index gained 1.1 percent to 13,116.93.
The weekend deal, reached after weeks of frantic negotiations, faces opposition from the progressive and hard-right wings of Biden and McCarthy's respective parties.
The basic framework of the deal lifts the debt ceiling, currently at $31.4 trillion, for two years -- enough to get past the next presidential election in 2024.
In return, Republicans secured some limits on federal spending over the same period.
Biden and McCarthy both say they believe the bill will pass the House and then move swiftly to the Senate.
Meanwhile, most large tech companies advanced early Tuesday, with shares of Facebook parent Meta and Apple both up more than one percent while Netflix rose nearly four percent.
The surge in Nvidia shares comes amid rising confidence in new generative AI breakthroughs, capable of delivering the computing heft needed to churn out complex content in just seconds from data centers around the world.
In topping $1 trillion in valuation, Nvidia joins a group of just five other companies, all US tech giants except Saudi Aramco.
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