Joe Biden has dared political opponents plotting legal challenges to his large-scale workforce vaccine mandates to “have at it” – as one Republican governor promised to fight the White House “to the gates of hell” over the new coronavirus rules.

A growing number of senior Republicans, including US senators, state governors and leading party officials, announced on Friday they would support or pursue legal avenues to try to block the president’s edict.

In an address at the White House on Thursday, Biden said his new orders would affect 100 million workers and help “turn the tide of Covid-19” in the US.

Among the most vocal was the South Carolina governor, Henry McMaster, who, in a tweet, painted the tussle over compulsory vaccination as a battle for personal freedoms.

“Rest assured, we will fight them to the gates of hell to protect the liberty and livelihood of every South Carolinian,” he wrote.

But on Friday, Biden did not appear to be flummoxed by the promised, largely partisan, resistance to his adminitration’s new workplace requirements.

The new rules are part of his six-pronged strategy to tackle the Delta-variant fueled resurgence of the pandemic.

“Have at it,” he said during a morning visit to a middle school in Washington on Friday, when a reporter asked for his response to Republicans threatening lawsuits.

“We’re playing for real here, this isn’t a game. And I don’t know of any scientist out there in this field that doesn’t think it makes considerable sense to do the six things I’ve suggested,” the president said.

Referring to Republicans such as Florida’s Ron DeSantis, currently embroiled in a lengthy legal fight over the right to ban mask mandates in schools, Biden added: “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.”

Republicans began seething over the new regulations almost as soon as the president finished delivering his remarks on Thursday afternoon, with some calling a vaccine mandate on private businesses with more than 100 workers “unconstitutional”.

Others, such as Arizona’s Republican governor Doug Ducey, insisted it would not survive legal scrutiny.

“This is exactly the kind of big government overreach we have tried so hard to prevent in Arizona – now the Biden-Harris administration is hammering down on private businesses and individual freedoms in an unprecedented and dangerous way,” Ducey said in a tweet.

“This will never stand up in court,” he added. “The vaccine is and should be a choice. We must and will push back.”

The partisan pushback came as the Centers for Disease Control and Prevention (CDC) put out studies on Friday one of which found that those who were not fully vaccinated in recent months were 11 times more likely to die of Covid-19 than the fully vaccinated. It was one of three major studies published by the federal agency that focus on the sustained high efficacy of the three Covid vaccines available in the US, against the highly infecious Delta variant.

Meanwhile, Ronna McDaniel, the chair of the Republican National Committee (RNC), said the party’s executive intended to file a lawsuit as soon as the mandate was enacted.

“Joe Biden told Americans when he was elected that he would not impose vaccine mandates. He lied,” she said in a statement.

“Like many Americans, I am pro-vaccine and anti-mandate. Many small businesses and workers do not have the money or legal resources to fight Biden’s unconstitutional actions and authoritarian decrees, but when his decree goes into effect, the RNC will sue the administration to protect Americans and their liberties.”

This is a reversal from Biden’s stance in July, when White House press secretary Jen Psaki said such mandates were “not the role of the federal government”.

In Texas, US senator Ted Cruz, who refused to certify Biden’s election victory on the night of the 6 January Capitol insurrection, seized on a retweet by Ron Klain, the White House chief of staff, that he insisted was an acknowledgement that the administration knew its actions were illegal.

The original message that Klain retweeted, by NBC journalist Stephanie Ruhle, referred to the emergency workplace safety rule by the occupational and safety and health administration (Osha) as “the ultimate work-around for the federal government to require vaccinations.”

The use of the phrase “work-around”, and Klain’s subsequent retweet of it, is a damaging admission, in Cruz’s view, because courts are allowed to evaluate the intention and purpose of policies.

“He said the quiet part out loud,” the senator tweeted. “Biden admin knows it’s likely illegal (like the eviction moratorium) but they don’t care.”

In a subsequent post, Cruz said: “The feds have no authority to force employers make their employees get vaccinated.”

Not all Republicans, however, are opposed to Biden’s move. Governor Phil Scott of Vermont retweeted the White House announcement of the new strategy and added: “I appreciate the president’s continued prioritization of vaccination and the country’s recovery as we move forward.

“As Vermont’s experience shows, vaccines work and save lives. They are the best and fastest way to move past this pandemic.”

Prominent health experts supported Biden.

One, Ashish Jha, dean of Brown University’s school of public health, told the New York Times: “It’s going to fundamentally shift the arc of the current surge. It’s exactly what’s needed at this moment.”