Mr. Manchin and Mr. Schumer are working to rally their party around their compromise, put forth in a surprise announcement on Wednesday. It would set aside $369 billion for climate and energy programs, as well as raise taxes on corporations and high earners, while lowering the cost of prescription drugs, extending health subsidies and reducing the deficit.

The abrupt announcement of a deal suggested a potential reversal of fortune for Mr. Biden and the Democrats, who had resigned themselves to the demise of the climate, energy and tax package. They had been preparing to push forward with a scaled-back pairing of the prescription drug pricing measure with an extension of expanded health care subsidies.

“This thing could very well, could not have happened at all,” Mr. Manchin declared on Thursday morning in an interview with Hoppy Kercheval, a West Virginia radio host. “It could have absolutely gone sideways, so I had to see if we can make this work.”

See omnystudio.com/listener for privacy information.