Progressive lawmakers emerged Tuesday from a meeting at the White House saying President Biden has taken charge of the negotiations over his sweeping domestic agenda, is offering specific spending recommendations — and has boosted the Democrats' hopes of winning an agreement in the coming weeks.

To create a sense of urgency, Biden is urging lawmakers to put their differences aside and get a bill to his desk before he and other top Democrats head to Glasgow for an international summit on climate change, a gathering that begins on Oct. 31.

"I felt that we're closer to a deal than I've ever felt before. I felt the president was engaged in the details of the negotiation in a way he hasn't been before,” said Rep. Ro Khanna (D-Calif.), one of nine House progressives who huddled with Biden in the Oval Office.

The comments came amid a busy day at the White House, where Biden was toiling to salvage his economic agenda. The president met separately with a pair of centrist senators — Joe Manchin (D-W.Va.) and Kyrsten Sinema (D-Ariz.) — who have resisted his economic plans, then hosted the larger group of progressives before rounding out the day with moderates of both chambers. Vice President Harris and Treasury Secretary Janet Yellen also participated.

The hands-on approach appeared to bear fruit. Manchin, returning from the White House, announced that he was set to launch focused talks with Sen. Bernie Sanders (I-Vt.), Sinema and Senate Majority Leader Charles Schumer (D-N.Y.) in an effort to break the months-long impasse that’s threatened to tank the massive social benefits package at the heart of Biden’s domestic policy wish list.

Manchin, who wants a much smaller spending package than Sanders and the progressives are pushing, predicted the negotiators could finalize a framework deal by the end of the week.

“If they come up with a framework, I think we're good to go,” Khanna said. “The hope is to get it before Glasgow.”

There remains some internal disagreement over how to cut the costs that Manchin and the moderates are demanding. Some Democrats want to limit the scope of the benefits package in order to focus on the party’s top priorities and fund them at length — ”to do fewer things better,” in the words of House Majority Leader Steny Hoyer (D-Md.).

Yet Khanna said his takeaway from the Biden meeting was just the opposite, predicting the scope would resemble that contained in the $3.5 trillion “family” benefits package initially championed by Biden. He said it would include a Medicare expansion, to include dental, vision and hearing benefits; an expansion of ObamaCare benefits; child care; universal preschool; paid family leave; and elder care.

“In the past he was speaking, sort of, values and of broad buckets; now he was really talking about line-items, how much is going to be in, how much may not be in, with a lot of specificity,” said Khanna, a close ally of Sanders. “And he seemed confident that he would be able to get the two holdout senators on board with a compromise framework.”

In a further sign of progress, liberals said they’re ready to accept the elimination of certain benefits they’d championed in the initial $3.5 trillion package.

Khanna said the Clean Electricity Performance Program, which is designed to slash utility emissions, is out of the package. He also indicated that liberals are ready to accept means-testing on the child tax credit — though the $60,000 threshold floated by Manchin is a “non-starter,” he said. And Progressive Caucus Chair Pramila Jayapal (D-Wash.) confirmed that Biden’s push for free community college would also be cut from the bill, though “there will be something for higher education.”

A Democratic source familiar with the progressives meeting confirmed that Biden was working off a piece of paper in the Oval Office meeting, rattling off specific dollar amounts for different parts of his Build Back Better package. For example, Biden said he was eyeing $350 billion for child care and universal pre-kindergarten, two of progressives’ top priorities.

“There is a recognition that there is a framework with Manchin. It’s not set in stone; the climate pieces are still very fuzzy,” said the Democratic source.

Biden also told progressive lawmakers that the next time he comes back to them, they will need to “trust” that he’s negotiated as far as he could with Manchin and the moderates, the source said.

Progressives feel “even more optimistic about getting to an agreement on a really transformational bill," Jayapal told reporters after the meeting. “I think the president has been working incredibly hard to get everybody to a place where we can move this forward and finish this process.

“The president is the inspirer. He is the closer. He is the convincer. He is the mediator in chief,” she added.

During the meetings Tuesday, lawmakers said, Biden continued to discuss a top-line number of between $1.9 trillion and $2.2 trillion — the same range he mentioned during a gathering with House Democrats in the Capitol several weeks ago. Jayapal signaled it was a range that progressives could live with, even though it’s significantly smaller than their original $3.5 trillion goal.

"Look, it's not the number that we want. We have consistently tried to make it as high as possible," Jayapal said. "But at the end of the day, the idea that we can do these programs, a multitude of programs, and actually get them going so that they deliver immediate transformational benefits to people is what we're focused on."

Sen. Jon Tester (D-Mont.), who joined the moderates meeting with Biden, said he’s surprised at how much movement there’s been in recent days.

“I think we’re making progress. I think we're making really good progress, better progress than I thought we were making,” Tester said after the moderates’ meeting. “I think I told one of you nothing’s happened in the last 10 days. There’s been a lot happening in the last 10 days — I just wasn’t aware of it.”

Aris Folley and Jordain Carney contributed.