National industry groups representing retail, truckers and independent businesses sued the Biden administration on Wednesday over its vaccine and testing requirements for private companies, claiming they would cause “irreparable harm.”The National Retail Federation, the National Federation of Independent Business and the American Trucking Associations, told the U.S. Court of Appeals for the 5th Circuit in their lawsuit that businesses would lose employees, incur “unrecoverable compliance costs” and face deteriorating conditions in “already fragile supply chains and labor markets” due to the requirements.The appellate court, considered one of the most conservative in the country, had already halted the vaccine and testing requirements pending review on Saturday, writing that the legal challenges “give cause to believe there are grave statutory and constitutional issues with the Mandate.”The court-ordered pause came in response to challenges from the Republican attorneys general of Texas, Louisiana, Mississippi, South Carolina and Utah, as well as several private companies. They argued that the Occupational Safety and Health Administration, which will enforce the mandates, exceeded its authority in an unconstitutional delegation of authority to the executive branch by Congress.National Retail Federation President Matthew Shay, in a statement Tuesday, said retailers are concerned about implementing the requirements during the busy holiday shopping season. The NRF, which represents the nation’s largest retailers, including Target and Walmart, sent a letter to President Joe Biden on Friday asking for an extension of the deadlines until after January, and requested a meeting with the administration on Tuesday.”We have consistently and repeatedly communicated our concerns about the practical challenges of meeting those arbitrary targets,” Shay said. “However, it appears that our only remaining course of action is to petition for judicial relief.”American Trucking Associations President Chris Spear, in a statement Wednesday, said the truckers told the Biden administration that the requirements “could have devastating impacts on the supply chain and the economy,” but the administration has “unfortunately, chosen to move forward despite those warnings.””So we are now, regrettably, forced to seek to have this mandate overturned in court,” Spear said.Labor Secretary Marty Walsh, in an interview with MSNBC on Thursday, said most truckers are exempt from the mandates because they are usually driving alone. OSHA has exempted workers who do not report to a workplace where others are present, as well as people working from home or exclusively outdoors.The National Federation of Independent Business, in its statement, said the mandates restrict the freedom of small business owners, calling the requirements a “clear example of administrative overreach.”White House Deputy Press Secretary Karine Jean-Pierre told reporters on Tuesday that the requirements would help businesses avoid labor shortages by preventing workers from getting sick with Covid. The requirements officially went into effect on Friday, starting the countdown for businesses with 100 or more employees to make sure their employees have received the shots required for full vaccination by Jan. 4. After that date, unvaccinated workers must submit a negative Covid test weekly to enter the workplace. Unvaccinated workers must start wearing masks indoors on Dec. 5.The Biden administration, in its response to the suits on Monday, asked the court to lift the pause, calling the states’ and companies’ claims of harm “premature” because the key deadline for vaccination or testing is not until January. The administration also warned the court that the halting the requirements “would likely cost dozens or even hundreds of lives per day.” The Labor and Justice Departments also argued that OSHA acted well within its authority as established by Congress.The administration faces a flurry of litigation over the vaccine and testing requirements. Republican attorneys general in at least 26 states have sued to halt the requirements in five different U.S. appeals courts. The Republican National Committee has also sued in the D.C. Court of Appeals.OSHA, which polices workplace safety for the Labor Department, developed the vaccine and testing requirements under emergency authority established by Congress. That authority allows OSHA to shortcut the normal process for developing workplace safety and health standards, which can take years.The Labor Department’s top lawyer, Seema Nanda, has said the administration is “fully prepared to defend this standard in court,” pointing to OSHA’s “authority to act quickly in an emergency where the agency finds that workers are subjected to a grave danger and a new standard is necessary to protect them.”OSHA, in its justification for the requirements on Friday, said the “extraordinary and exigent circumstances” of the pandemic required the agency to “immediately address the grave danger that COVID-19 poses to unvaccinated workers by strongly encouraging vaccination.”As the legal challenges mount, the cases will soon be consolidated in one court through random selection among the jurisdictions where petitions were filed. The Justice Department said in a filing Monday that the random selection process is expected take place on or around Nov. 16.David Vladeck, a professor of law at Georgetown University, told CNBC on Monday there’s a “high probability” that the case will end up before the Supreme Court.The White House, for its part, is telling businesses to press ahead with the requirements even as the legal drama plays out in the nation’s federal appeals courts.”People should not wait,” Jean-Pierre told reporters during a briefing on Monday. “They should continue to move forward and make sure they’re getting their workplace vaccinated.”CNBC’s Lauren Thomas contributed to this article.