WASHINGTON (AP) — President Joe Biden called some Republican governors "cavalier" on Friday for resisting his call for far-reaching new federal coronavirus vaccine requirements he hopes will curb the surging delta variant.

Biden visited a public school just a short drive from the White House to make the case for new rules he set out a day earlier that could impact 100 million Americans.

He also pushed back against Republicans, and some union officials, who say he is overreaching his authority. Biden said they were shirking their responsibility to young Americans.

"I am so disappointed that particularly some Republican governors have been so cavalier with the health of these kids, so cavalier with the health of their communities," Biden said during a visit to Brookland Middle School in northeast D.C. "This isn't a game"

The new federal vaccine requirements would affect private-sector employees as well as health care workers and federal contractors.

First lady Jill Biden, who joined the president for the school visit, echoed Biden's message that getting more Americans vaccinated was essential to keep schools open and helping working parents.

"We owe them a promise to keep their schools open as safe as possible," the first lady said. "We owe them a commitment to follow the science. We owe them unity, so that we can fight the virus, not each other."

Speaking at the White House Thursday, Biden sharply criticized the tens of millions of Americans who are not yet vaccinated, despite months of availability and incentives.

"We've been patient. But our patience is wearing thin, and your refusal has cost all of us," he said, all but biting off his words. The unvaccinated minority "can cause a lot of damage, and they are."

Republican leaders — and some union chiefs, too — said Biden was going too far in trying to muscle private companies and workers, a certain sign of legal challenges to come.

Gov. Henry McMaster of South Carolina said in a statement that "Biden and the radical Democrats (have) thumbed their noses at the Constitution," while American Federation of Government Employees National President Everett Kelley insisted that "changes like this should be negotiated with our bargaining units where appropriate."

Asked on Friday about potential legal maneuvering to stop enforcement of the new vaccine requirements, Biden shot back: "Have at it."

There have also been strong words of praise for Biden's efforts to get the nation vaccinated from the American Medical Association, the National Association of Manufacturers and the Business Roundtable — though no direct mention of his mandate for private companies.

The expansive rules mandate that all employers with more than 100 workers require them to be vaccinated or test for the virus weekly, affecting about 80 million Americans. And the roughly 17 million workers at health facilities that receive federal Medicare or Medicaid also will have to be fully vaccinated.

Biden is also requiring vaccination for employees of the executive branch and contractors who do business with the federal government — with no option to test out. That covers several million more workers.

Just two months ago Biden prematurely declared the nation's "independence" from the virus. Now, despite more than 208 million Americans having at least one dose of the vaccines, the U.S. is seeing about 300% more new COVID-19 infections a day, about two-and-a-half times more hospitalizations, and nearly twice the number of deaths compared to the same time last year. Some 80 million people remain unvaccinated.

In addition to the vaccination requirements, Biden moved to double federal fines for airline passengers who refuse to wear masks on flights or to maintain face covering requirements on federal property in accordance with Centers for Disease Control and Prevention guidelines.

He announced that the government will work to increase the supply of virus tests, and that the White House has secured concessions from retailers including Walmart, Amazon and Kroger to sell at-home testing kits at cost beginning this week.

The administration is also sending additional federal support to assist schools in safely operating, including additional funding for testing. And Biden called for large entertainment venues and arenas to require vaccinations or proof of a negative test for entry.

The requirement for large companies to mandate vaccinations or weekly testing for employees will be enacted through a forthcoming rule from the Occupational Safety and Health Administration that carries penalties of $14,000 per violation, an administration official said.

The rule will require that large companies provide paid time off for vaccination.

Meanwhile, the Centers for Medicare & Medicaid Services will extend a vaccination requirement issued earlier this summer — for nursing home staff — to other healthcare settings including hospitals, home-health agencies and dialysis centers.

Separately, the Department of Health and Human Services will require vaccinations in Head Start Programs, as well as schools run by the Department of Defense and Bureau of Indian Education, affecting about 300,000 employees.

Biden's order for executive branch workers and contractors includes exceptions for workers seeking religious or medical exemptions from vaccination, according to press secretary Jen Psaki. Federal workers who don't comply will be referred to their agencies' human resources departments for counseling and discipline, to include potential termination.

Biden has encouraged COVID-19 vaccine requirements in settings like schools, workplaces and university campuses. On Thursday, the Los Angeles Board of Education v oted to require all students 12 and older to be fully vaccinated in the the nation's second-largest school district.

Walmart, the nation's largest private employer, said in late July it was requiring all workers at its headquarters in Bentonville, Arkansas, as well as its managers who travel within the U.S., to be vaccinated against COVID-19 by Oct. 4. But the company had stopped short of requiring shots for its frontline workers.

CVS Health said in late August it would require certain employees who interact with patients to be fully vaccinated by the end of October. That includes nurses, care managers and pharmacists.

In the government, several federal agencies have previously announced vaccine requirements for much of their staffs, particularly those in healthcare roles like the Department of Veterans Affairs, and the Pentagon moved last month to require all servicemembers to get vaccinated. Combined, the White House estimates those requirements cover 2.5 million Americans. Thursday's order is expected to affect nearly 2 million more federal workers and potentially millions of contractors.

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Associated Press writer Aamer Madhani contributed reporting.