Biden administration plans to get US companies with 100 or more workers to vaccinate their staff or bring in regular tests have been welcomed by public health groups but slammed by Republicans and trade groups, who claim government overreach with negative economic consequences.

Such divided reaction to the rules announced last week mirrors much of America’s problematic vaccine rollout, where social and political headwinds have seen vaccination take-up slow down worryingly. US vaccination rates are some of the lowest in industrialized countries where the vaccine is readily available.

Subject at least to a temporary stay issued by a circuit court in New Orleans on Saturday, the new rule from the Occupational Safety and Health Administration (Osha) will take effect on 4 January.

It requires that large companies either ensure employees have been vaccinated or regularly administer Covid-19 tests and require masks at work for those who refuse to get the shot.

The rule will affect an estimated 84 million workers.

The Centers for Medicare & Medicaid Services also issued a rule requiring healthcare workers to be vaccinated by the same deadline, with no option for weekly testing rather than vaccination. That will affect 76,000 providers and more than 17 million workers.

The administration also extended a deadline for federal contractors to comply with the same sort of rule – vaccination without the testing option – from 8 December to 4 January.

“Too many people remain unvaccinated for us to get out of this pandemic for good,” Joe Biden said in a statement.

But the rules sparked new backlash from Republican lawmakers and conservative groups who described the measures as unconstitutional. Republican governors or attorneys general in 15 states plan to file lawsuits against the mandate, according to the Associated Press.

“This rule is garbage,” South Carolina’s attorney general, Alan Wilson, a Republican, said, according to the AP. “It’s unconstitutional and we will fight it.”

Celebrating the Saturday ruling in Louisiana, the state attorney general, Jeff Landry, said: “The president will not impose medical procedures on the American people without the checks and balances afforded by the constitution.”

While courts have largely declined to block state and local vaccine mandates, the federal government “has more constraints on it than state and local governments do when it comes to public health and vaccination”, said Lindsay Wiley, a public health law professor at American University.

On whether the Osha rule could be overturned, Wiley said: “It’s difficult to predict, in part because the environment has become so politicized.”

Plaintiffs could also seek to file lawsuits in circuits with conservative judges appointed by Donald Trump, Wiley said.

Lawrence Gostin, a global health law expert at Georgetown Law, tweeted earlier this week that “Biden is on rock-solid legal ground. He’s acting to protect the US workforce and will get us all back to normal sooner.”

But groups such as the National Retail Federation (NRF), the country’s largest retail trade group, condemned the Osha rule because they said it places an unreasonable burden on businesses during the holiday season, which for many ventures is the busiest time of the year.

The NRF is requesting an extension of the deadlines, though Edwin Egee, a vice-president of the group, did not provide a preferred date.

“NRF members have for months taken extraordinary efforts to distribute the vaccine, to incentivize the vaccine. We have been, and will continue to be, very much in favor of the vaccine and its efficacy,” Egee said.

Republicans have also warned that the vaccine requirements could cause employees to quit. If faced with a mandate, 11% of the unvaccinated said they would be most likely to get the vaccine and 46% said they would opt for weekly testing, according to an October survey from the Kaiser Family Foundation (KFF). More than a third of unvaccinated workers said they would quit if their employer required them to get a vaccine or get tested weekly. But that amounts to just 5% of all adults in the US.

“When we are looking at the bigger picture amongst all adults … it’s a pretty small share of the population,” said Lunna Lopes, senior survey analyst for KFF.

There is evidence that workers often opt to get vaccinated rather than lose their jobs. For example, Houston Methodist hospital required 25,000 workers to get a vaccine by 7 June, the Conversation, a non-profit news organization, reported. Before the mandate, about 15% of employees were unvaccinated. By mid-June, that had dropped to 3%.

David Michaels, a former Osha chief now a professor of public health at George Washington University, argued the new rules would help businesses who wanted to institute requirements but were constrained by state and local rules or feared litigation.

“This actually allows employers to do what they want to do and blame the federal government,” said Michaels, who has advised the Health Action Alliance, a coalition of corporations such as Starbucks and Amazon and non-profits such as the CDC Foundation and the Ad Council aimed at promoting Covid-19 vaccination and prevention.

The rules will make the workplaces safer, Michaels said.

“The retail industry should give a gift to the American people and start to be supportive of vaccination requirements,” Michaels said. “That’s the only way that we will save lives and return to normalcy. It’s outrageous to ask for an exception to a public health measure.”