The Biden administration is trying to build support for proposals to overhaul the nation’s rickety child care system as it pushes Congress to embrace a $3.5 trillion plan to expand social safety programs and looks for ways to combat ongoing labor shortages.

In a new report released on Wednesday, the Treasury Department painted a dire picture of child care in America, outlining what it called failures by the private sector to provide high-quality care at affordable prices and making the case that the federal government must do more to help families care for their children.

“This is not just happenstance — sound economic principles explain why relying on private money to provide child care is bound to come up short,” the report said.

The Biden administration has already disbursed nearly $40 billion to help child care providers and day care centers through funds that were approved in the American Rescue Plan, which Congress passed earlier this year. The Treasury Department has also been distributing monthly advance child tax credit payments to families with children.

On Wednesday afternoon, Vice President Kamala Harris visited the Treasury Department to make the case for more child care funding and described the lack of quality care in the country a national emergency.

“Childcare remains too expensive and out of reach for far too many working families in our country,” Ms. Harris said, adding that other advanced economies invest more in child care than the United States. “We need to bring costs down with a significant investment in our child care industry.”

Ms. Yellen made the case for bold investments in both personal and economic terms. She recalled that 40 years ago when she was returning to work after her son was born, she placed an advertisement in a local newspaper offering a few dollars more than the standard wage for a babysitter because the work was so important. She reflected on the fact that she was fortunate enough to be able to pay a higher wage and said that if she had not been able to find quality care at that time in her career, she might not be Treasury Secretary today.

Ms. Yellen lamented that most families must bear the cost of child care when they are young and their earnings are low. She said that public investment is needed because of all of the economic benefits that come when parents have access to quality care for their children.

“The free market works well in many different sectors, but child care is not one of them,” Ms. Yellen said. “Child care is a textbook example of a broken market.”

Mr. Biden’s plan includes child care subsidies for low- and middle-income families, universal prekindergarten for children who are 3 and 4 years old and a permanent expansion of the child and dependent care tax credits.

The Treasury report argues that families are currently spending about 13 percent of their income to pay for child care costs for a child under the age of 5. Despite the high costs, child care providers tend to be poorly compensated.

The patchwork nature of the child care system often creates incentives for a parent to leave the labor force, losing access to health insurance and retirement benefits. The United States is currently grappling with a labor shortage, and the Biden administration views bolstering access to child care as a way to get people back to work.

“In basic economic terms, the president’s proposals will expand both demand for and supply of child care,” the report said. “With expanded demand, more children will have access to the rich early experiences and more parents will be able to choose to remain in the labor force.”