WASHINGTON — Senator Joe Manchin III of West Virginia, who had been the chief Democratic holdout on a climate, energy and tax increase package that is the backbone of his party’s agenda, said on Thursday that he had relented and agreed to sign on after concluding that it would help combat inflation, as top Democrats toiled to rally support to quickly pass the measure.
Mr. Manchin said the surprise compromise began taking shape only days after he and Senator Chuck Schumer, Democrat of New York and the majority leader, had a bitter break during intense negotiations on the plan, when the West Virginian informed Mr. Schumer that he could not support a package with new climate spending or tax proposals this summer amid skyrocketing inflation.
“You know how our tempers get a little bit ahead of us at times,” Mr. Manchin, who is isolating after testing positive for the coronavirus this week, told reporters during a virtual news conference.
Mr. Schumer, he said, had “turned the dogs loose” on him two weeks ago after he said he could not commit to the plan. But four days later, the two patched up their split and sent their staffs back to the negotiating table to find a version both could accept.
By Wednesday, they had struck a deal. The critical concessions that ultimately won Mr. Manchin’s support included jettisoning billions of dollars’ worth of tax increases he opposed and winning a commitment from President Biden and Democratic leaders to enact legislation to streamline the permitting of energy infrastructure. That could ease the way for a shale gas pipeline project in West Virginia in which Mr. Manchin has taken a personal interest.
“I’m saying straight to you, without permitting reforms, without the ability for America to do what it does best — produce — there is no bill,” he said on Thursday morning, speaking to Hoppy Kercheval, a West Virginia radio host. “That is totally agreed upon and understood.”
In a private caucus meeting on Thursday morning, Mr. Schumer began laying the groundwork for what promises to be an arduous process of steering the compromise through the evenly divided Senate, made more difficult by the chamber’s arcane rules, Democrats’ bare-minimum majority and a coronavirus surge among senators.
He counseled Democratic senators that they had the opportunity to deliver on their longstanding ambitions to combat the threat of climate change and allow Medicare, for the first time, to negotiate the prices of prescription drugs, pushing down costs for patients.
“It will require us to stick together and work long days and nights for the next 10 days,” Mr. Schumer told his colleagues, according to a Democrat in the room, who disclosed details of the private meeting on the condition of anonymity. He added: “We will need to be disciplined in our messaging and focus. It will be hard. But I believe we can get this done.”
The abrupt announcement of a deal held out the promise of a major reversal of fortune for Mr. Biden and Democrats, who had resigned themselves to the demise of the climate, energy and tax package and were preparing to push forward with a bill that would pair the prescription drug pricing measure with an extension of expanded health care subsidies.
Should the compromise hold and survive consideration by both the Senate and the House, it would allow them to enact major legislation only weeks before the midterm congressional elections to address health care costs, climate change and inflation — all while fulfilling longstanding promises to tax the rich and reduce the deficit.
But the fate of the measure remained on shaky ground.
It was not clear whether it would have the unanimous support among Democrats needed to pass. Senator Kyrsten Sinema, Democrat of Arizona and another holdout on her party’s domestic policy package, skipped the Democratic caucus meeting on Thursday and would not comment on the bill or indicate whether she planned to support it.
“She’s reviewing text and will need to review what comes out of the parliamentarian process,” a spokeswoman said.
Ms. Sinema has in the past opposed one element of the agreement: a proposal to change a preferential tax treatment for income earned by venture capitalists.
Even if it can win passage in the Senate, the measure would also need to pass the House, where Democrats can spare only a few votes given likely unanimous Republican opposition.
Democratic leaders aimed to hold votes on the legislation in the Senate as early as next week, before the chamber is scheduled to leave for the annual August recess. But they will have to navigate the legislation through a series of parliamentary and procedural challenges, including a set of rapid-fire, politically fraught amendments Republicans can force before a final vote.
And with Republicans expected to unanimously oppose the measure, all 50 senators who caucus with Democrats will need to be present and back the package for it to pass the Senate, along with the tiebreaking vote of Vice President Kamala Harris.
Senator Richard J. Durbin of Illinois, the No. 2 Democrat, said on Thursday that he had tested positive for the coronavirus, becoming the latest senator forced to isolate this month.