Biden, Schumer and Manchin had a "productive discussion" and continued to make progress, the White House said in a statement after the meeting, without elaborating.
Democrats have struggled to agree on a framework of $2 trillion or less that will allow the House of Representatives to move forward next week on a $1 trillion bipartisan infrastructure bill and set the stage for passage of Biden's larger "Build Back Better" package.
The divisions threatened to derail Biden's agenda on social spending and climate change and embarrass the U.S. president as he prepares to attend the opening of a global climate summit in Glasgow that begins on Oct. 31.
Schumer and Manchin were meeting to finalize some of the particulars. "I'm optimistic that we can do that," Pelosi said.
Asked if votes on the two bills would be held in the coming week, Pelosi said, "That's the plan."
Disagreements over the scale of the larger package have held up Biden's domestic agenda, with progressive Democrats in the House refusing to vote for the infrastructure bill, which has already been passed by the Senate, until a deal is reached on social programs and climate change.
Moderate Democrats, most notably Manchin and Senator Kyrsten Sinema, had objected to the original $3.5 trillion price tag and some provisions of the latter bill. Republicans oppose the measure, but 19 in the Senate voted in support of the infrastructure legislation.
The White House is seeking to get Manchin to support roughly $2 trillion in spending, up from Manchin’s $1.5 trillion figure, according to two sources familiar with the discussions.
The White House and Democratic leaders need the money to help keep the party unified as they slim down the legislation and make painful cuts to party priorities, like Medicare expansion, paid family leave and free community college.
Sinema has opposed a hike in the corporate tax rate that had been a main source of funding for the bill, but Pelosi said losing that would not stand in the way of raising the roughly $2 trillion needed to pay for the programs.
Pelosi said lawmakers have an array of options to fund the spending bill even without the corporate tax rate hike, including better tax enforcement, a so-called billionaires tax and international tax harmonization.
Senators were writing that tax proposal on Sunday and would introduce it Monday, Pelosi said.
Treasury Secretary Janet Yellen said on the CNN program she anticipated no problems in funding the bill.
"All in all, it should be relatively straightforward to raise the revenue necessary to pay for this bill," Yellen said.
The White House is also pressing Manchin to agree on a number of environmental measures after the senator, from coal-producing West Virginia, opposed a centerpiece of the plan that would reward utilities that invest in renewable fuels and penalize those that do not.
Democrats are considering a flurry of options, including boosting production tax credits for nuclear power and enhancing credits for carbon sequestration projects, the sources said.
Addressing climate change is a health issue, a jobs issue, a security issue and a values issue for Democrats, Pelosi said.
"We will have something that will meet the president's goal," Pelosi said. "I'm very confident about that, even though it will be different than what we originally proposed."
(Reporting by Doina Chiacu, Michael Martina, Jarrett Renshaw and Richard Cowan; Additional reporting by Chris Gallagher; Editing by Hugh Lawson, Grant McCool and Daniel Wallis) ((firstname.lastname@example.org; 202-898-8322;))