WASHINGTON — Senator Joe Manchin III of West Virginia had breakfast with President Biden at his home in Wilmington on Sunday, hashing out concerns about the expansive domestic policy bill taking shape in Congress.

The senator was back at the Capitol on Monday, where his fellow Democrats peppered him with all manner of entreaties. Senator Kirsten Gillibrand of New York wanted his backing for a federal paid leave proposal that he has resisted. A group of Democrats implored him to drop his opposition to a fee on methane emissions. Both Democratic senators from Georgia wished he would take another look at a Medicaid expansion proposal that would help their states.

By Tuesday evening, Mr. Manchin was huddling in the basement with Senator Bernie Sanders of Vermont, the chairman of the Budget Committee, whose proposal to expand Medicare he has panned.

As Democrats push for a compromise on their marquee domestic priority, Mr. Manchin, the most outspoken holdout on the plan and a crucial swing vote, has become the target of intense personal lobbying by his colleagues. In private meetings, huddles on the Senate floor and phone calls, he has faced renewed pressure to abandon his opposition.

“My dad always said, ‘If you can say no with a tear in your eye, you might be OK,’ and I’ve been crying a lot lately,” Mr. Manchin said at an event on Tuesday with the Economic Club of Washington, adding that there was “nothing fun about” his position.

In an evenly divided Senate, the fate of Mr. Biden’s domestic agenda could hinge on any one Democratic senator willing to withhold his or her vote. And while Mr. Manchin is not the only centrist who has raised concerns, his lengthy bill of particulars against the legislation has made him a popular target for lawmakers pressing to salvage key provisions of the rapidly shrinking plan.

For Senate Democrats, it is perhaps the most time-tested stage of negotiations: the courtship of a lawmaker who holds a crucial swing vote. Despite his protestations, Mr. Manchin seems to relish the role, even as he waves off questions about details of the talks and rumors that he might soon leave the Democratic Party.

“Do you think by having a D or an I or an R is going to change who I am?” he said on Tuesday. “I don’t think the R’s would be any more happier with me than D’s are right now.”

“I don’t know where in the hell I belong,” he added, drawing laughter from the audience.

In recent days, the senator has publicly objected to major components of the bill, including the expansions of Medicare and Medicaid, the federal paid leave program, two major climate provisions and a proposal to empower the I.R.S. to obtain data for customers’ bank accounts as part of an effort to crack down on unpaid taxes and raise revenue to pay for the package.

Mr. Manchin, whose demand that the overall package not exceed $1.5 trillion has driven a frenzied effort to cut the cost of the bill, has maintained that he is keeping an open mind out of fairness to Mr. Biden and Democratic leaders.

But he has proved unyielding on many of progressives’ most cherished priorities, such as Mr. Sanders’s drive to add vision, hearing and dental benefits to Medicare.

“Bernie and I have met the last three days for at least an hour a day, getting to know each other differently than we ever did before,” Mr. Manchin said he had told Mr. Biden on Sunday. “He has my respect. I know who he is, and where he’s coming from. I just respectfully disagree.”

That resistance has not stopped Democrats from trying to sway him. These days, Mr. Manchin can usually be found huddled with colleagues who are seeking his support — or to change his mind — on a component of the social policy bill. On Monday evening, it was Senator Chuck Schumer of New York, the majority leader, along with Senators Thomas R. Carper of Delaware, Maria Cantwell of Washington, Ron Wyden of Oregon and other climate hawks seeking to salvage a fee on methane emissions and other spending to which Mr. Manchin had objected.

Representative Richard E. Neal of Massachusetts, the chairman of the Ways and Means Committee, said he had sought a meeting with Mr. Manchin to discuss how to increase taxes to pay for the plan. He reminded reporters that the two had worked together on pension legislation.

After his breakfast with Mr. Biden and Mr. Schumer, Mr. Manchin fielded a call from Representative James E. Clyburn of South Carolina, the No. 3 House Democrat, who urged him to support a proposal to cover the cost of expanding Medicaid in states that had not done so under the Affordable Care Act. Mr. Manchin has said it would be unfair for the federal government to cover those costs for some states, when others like West Virginia have expanded their Medicaid programs and received only a 90 percent subsidy.

Democrats have good reason to court Mr. Manchin’s support. They remember how difficult it was to win his vote on the $1.9 trillion pandemic aid plan enacted this year, including his last-minute effort to slash the size of the unemployment benefits included in the measure. (While Mr. Manchin ultimately voted yes after winning the concessions he sought, the grueling negotiations led to the longest open Senate vote in modern history.)

But the episode also proved that he could be swayed — albeit not as far as his liberal colleagues would like — offering negotiators a glimmer of hope.

“Joe is not a bad guy — he’s a friend,” Mr. Biden said, speaking during a CNN town hall last week. “And he’s always, at the end of the day, come around and voted for it.”

Some Democrats have said they appreciate Mr. Manchin’s willingness to roll up his sleeves and negotiate. Senator Kyrsten Sinema, Democrat of Arizona and another holdout on the legislation, has preferred to keep her preferences confined to private talks with the White House and a limited circle of colleagues.

“He doesn’t negotiate in public,” said Representative Henry Cuellar, Democrat of Texas, adding that he had also spoken with Mr. Manchin recently. “But he gives where he stands.”

Catie Edmondson contributed reporting.