News of the mandates prompted Gov. Henry McMaster of South Carolina to say he would fight Mr. Biden and his party “to the gates of hell.”

Several Republican governors vowed to go to court to challenge the constitutionality of the rules that affect two-thirds of American workers, setting the stage for one of the nation’s most consequential legal battles over public health since Republicans sued to overturn the Affordable Care Act…

Gov. Brian Kemp of Georgia suggested that he might sue to “stop this blatantly unlawful overreach by the Biden administration.” Gov. Kay Ivey of Alabama referred to the rules as “outrageous, overreaching mandates.”

And in Florida, where a judge on Friday allowed a ban on school mask mandates to remain in place as a legal challenge works its way through the courts, Gov. Ron DeSantis said in a fund-raising email that Mr. Biden had “declared war” on the rule of law and millions of Americans’ jobs by issuing the vaccine requirements.