The impasse jeopardizes Mr. Biden’s reputation as a dealmaker — he had campaigned on his ability to capitalize on nearly four decades of Senate experience to helm negotiations and unite his party’s narrow majorities in both chambers. Mr. Biden had poured weeks of work into talks with Mr. Manchin, inviting the senator for breakfast at his Delaware home in October and insisting that the West Virginian could ultimately be swayed.

At stake is what Mr. Biden has hailed as transformative, New Deal-style legislation that would touch virtually every American life from birth to death, from subsidies for child care to price controls for prescription drugs to funding for the construction and maintenance of public housing.

Failure to pass the measure also would deal a setback to vulnerable Democratic lawmakers bracing for what is expected to be a challenging midterm campaign in the coming months. They had hoped that passage of the bill would help their political standing, given that Republicans are widely expected to reclaim control of the House.

“After months of negotiations, one Democratic U.S. senator has now summarily walked away from productive negotiations,” said Representative Abigail Spanberger, a Virginia Democrat who represents a swing district. “That is unacceptable, and we cannot act like this moment is the end. Children, families and the future of our planet are counting on us.”

The legislation, originally sketched out as a $3.5 trillion budget blueprint, had already been curtailed substantially to satisfy Mr. Manchin and a few other centrists, through months of laborious negotiations.

As it is, an expanded $300 monthly payment to most families with children, which Mr. Manchin voted for as part of the $1.9 trillion pandemic aid package in March, will lapse at the end of the year without an extension included in the package. Long-sought promises to patch gaps in the American health care system, from expanding coverage to an estimated 3.4 million Americans to improving Medicare benefits and regulating drug prices, will go unfilled.

The senator’s staff informed party leadership and the White House of his position Sunday morning before his televised appearance, according to one official familiar with the outreach, who spoke on condition of anonymity. But the tone of Ms. Psaki’s statement was a sharp break from months of White House handling of Mr. Manchin — and clearly expressed surprise and a sense of betrayal.