But Biden’s hours and hours of meetings don’t just reflect the precarious moment in which his presidency finds itself. They underscore the heavy reliance his White House has placed on an inside game, rather than the bully pulpit, to dislodge recalcitrant holdouts and move their agenda.

"The president is a longtime policy guy and relationship guy. So he brings both kinds of skills to his work" to corral his party behind a trillion-dollar-plus package of progressive priorities, said Biden's former primary rival Sen. Elizabeth Warren (D-Mass.).

Warren acknowledged, however, that Biden's level of influence over Sens. Joe Manchin (D-W.Va.) and Kyrsten Sinema (D-Ariz.) — both of whom met with Biden on Tuesday — remains to be seen: "We'll know the answer to that when we make it across the finish line and assess what we’ve got."

Biden met Tuesday afternoon with Sens. Jon Tester (D-Mont.), Catherine Cortez Masto (D-Nev.) and Mark Warner (D-Va.), along with House progressives and moderates.

"We just need to get to a number," Tester said after returning from the White House. "I think that he likes all the programs but I think everybody's negotiable at this point."

Biden told progressives that tuition-free community college would likely be cut from the final package and the child tax credit may only be extended for a single year, according to a source familiar with the meeting.

Rep. Pramila Jayapal, chair of the Congressional Progressive Caucus, said after the meeting that tuition-free college is "probably going to be out," and certain climate priorities were "challenging."

"At this point we don't have a certainty on the final thing, but what we're hearing is good," Jayapal said. "We feel like the vast majority, if not all, of our priorities are in there, in some way, shape or form.”

As Biden has worked on lawmakers in private — sometimes not putting a hard stop on his schedule so as not to stifle progress — he’s largely, though not entirely, resisted riskier public pressure campaigns that could backfire and are viewed as against his nature.

Often, Biden has had just a single public event each day. Occasionally, there’s been no public interfacing at all. Eight times since Labor Day, the daily guidance issued by the White House has included only private meetings with Biden.

A planned barnstorming of the country to sell the Build Back Better platform this summer was overshadowed by the chaotic U.S. withdrawal from Afghanistan. And congressional uncertainty amid infighting among Democrats on opposite poles of the party has overshadowed continuing trips by Cabinet officials and commandeered the media narrative in Washington.

While Biden has held public events around the agenda, he has not done a formal press interview on it since Labor Day. On Wednesday, he will take a trip to his hometown of Scranton, Pa., to discuss the benefits of the legislative proposals, and on Thursday he will participate in a town hall broadcast on CNN.

“The President won the most votes in history running on his Build Back Better agenda, unveiled the formal proposal in his first address to a joint session of Congress, and has made his case across the country ever since – along with his cabinet – which is deeply resonating with the American middle class," White House spokesman Andrew Bates said.

Over the weekend, Biden called Sen. Bob Casey (D-Pa.) to discuss the upcoming trip, according to the senator, who is working on expanding care for older people and people with disabilities.

“He wanted to get some suggestions about issues we should focus on, while we’re there,” Casey said.

Still, inside the White House, the lower-key strategy has been seen as a necessity: Democrats have such slim congressional majorities that Biden, Senate Majority Leader Chuck Schumer and Speaker Nancy Pelosi have essentially no margin for error. That has put far more of the president’s focus on convincing a relatively small number of lawmakers to agree to details of the package, rather than using his time to sell policies that the general public supports.

Chief among that small number of lawmakers are Manchin and Sinema, who remain resistant to the range of $1.9 trillion to $2.2 trillion that Biden and progressive lawmakers have discussed as a compromise top line for the social spending bill.

"I'm told that they've given signs on the parking spaces for these two senators at the White House, that they're there so often,” Senate Majority Whip Dick Durbin (D-Ill.) said of Manchin and Sinema. “This president has been engaged from the start, in working with all the leaders, and particularly with those two senators."

As he does that, Biden has labored to project a sense of optimism about his progress. White House officials say they’re encouraged by what they described as the accelerated pace of the talks, even as the Oct. 31 timetable appears exceedingly ambitious.

Another explanation for the approach was baked in long ago. Biden is a 36-year veteran of the Senate with a heightened sense of his own negotiating instincts and abilities to move major legislation through the chamber. A self-admitted schmoozer, he has avoided doing much to shame Manchin and Sinema, preventing many details from their conversations and about his own preferences from spilling into public view.

“There’s a lot of complaining about what the message has been on this package, but when you’re trying to fight for every vote, the coverage inevitably becomes about the process and numbers,” said John Podesta, a top aide to former Presidents Barack Obama and Bill Clinton and a major climate activist. “When you are inside talking one-on-one to members trying to convince people to stay with you or come on board it’s very hard to create a press environment which is different from what they’ve got.”

Biden has resumed his in-person meetings with Congress’ return to Washington, including Tuesday sit-downs that involved Vice President Kamala Harris and Treasury Secretary Janet Yellen. There's a deepening acknowledgment that he has to hurry.

“They really are now in a circumstance where they will take on more and more water unless they can close the framework,” Podesta added. “I think they’ll do it. But it’s not like they have forever. We’re talking about this week or next week.”

In his meetings, Biden has spent a considerable amount of time on the party’s collective sense of urgency, aides and allies said, telling members of his party that they simply have to deliver. The conversations have at times been crisp, with Biden telling some Democratic skeptics that in order to be part of the negotiating process, they need to articulate policies that they are for and not just what they oppose — a message similar to the one Sen. Bernie Sanders (I-Vt.) has delivered to Manchin and Sinema.

Biden’s goal has been to help establish broad areas of agreement before filling in the specifics. At the same time, Biden has repeatedly cautioned his senior aides and officials not to rely on generalizations, and to prepare recommendations based on data and input from the lawmakers about their states and districts.

He has stolen bits of face time with lawmakers wherever he can, keeping members back after bill signings, for example, to sound them out, and gathering with them in their districts when he’s been on the road. Moving beyond sticking points has been a challenge, and Biden is known to implore lawmakers to step back and ignore a particular area and to temporarily focus on others where they might be able to make progress.

“When you see him artfully and deftly manage these hard conversations with members and guide them into a productive place, it helps remind you there is room for optimism and there is a pathway here,” said Louisa Terrell, director of the White House Office of Legislative Affairs.

Daniel Lippman contributed to this report.