The Dow Jones Industrial Average was up 113.37, or 0.4%, at the end of trading after climbing as high as 300 points earlier in the day. The S&P 500 also climbed 0.47% and the Nasdaq Composite gained 0.33%.
Stocks that would benefit from the widespread lifting of coronavirus restrictions and resuming of economic activity responded positively to the optimism surrounding stimulus talks. Carnival stock gained 3.29% and American Airlines increased 1.91% while retailers Kohls and Nordstrom grew 6.72% and 1.15% respectively.
Tuesday's gains came after markets fell Monday amid reports Pelosi and Treasury Secretary Steven Mnuchin were not close to a deal, however, a spokesman for Pelosi said later in the day that they "continued to narrow their differences" ahead of Tuesday's meeting.
"Hopefully by the end of the day, we'll know where we all are," Pelosi said. "But I'm optimistic."
Pelosi also said that a 48-hour deadline she gave the administration on Sunday was not a deadline for a deal but rather "was a day that we would have our terms on the table to be able to go to the next step."
Netflix stock also slid 1% after the streaming service reported 2.2 million net new subscribers in the third quarter, after adding 10 million subscribers in the first two quarters as people were forced inside due to the pandemic.
"Because the pandemic has been long lasting and some states have loosened their quarantine restrictions, Netflix's U.S. subscriber growth ... is reaching saturation," eMarketer analyst Ross Benes told MarketWatch.