The fate of President Joe Biden’s COVID-19 vaccine mandate for private employers could come down to the bounce of a ping-pong ball.

Republican officials in 27 states, employers and several conservative and business organizations filed challenges to the mandate in numerous federal courts shortly after the U.S. Occupational Safety and Health Administration released details of the emergency rule Nov. 4. Several unions also filed challenges in other federal courts, contending it doesn’t go far enough.

The cases are expected to be consolidated under one of the circuit courts in a decision expected as soon as Tuesday.

Which federal court ends up with the case could determine whether the requirement gets tossed out, a reflection of how the judiciary has become politicized in recent years. The New Orleans-based 5th U.S. Circuit Court of Appeals, where a majority of justices were nominated by Republicans, issued a ruling putting the mandate on hold.

Allison Orr Larsen, a professor at William & Mary Law School, coauthored a study published this year that found growing partisanship in federal judicial decisions. For decades, the study found that rulings on cases in which all judges in a circuit weighed in generally were not decided along party lines based on the presidents who appointed the judges.

“We did see a concerning spike starting in 2018 that led us to wring our hands,” Larsen said in an interview.

The increasing partisanship in a branch of government that is supposed to be blind to partisan politics was seen in judges appointed by presidents of both parties, but Larsen said it’s not clear why that was or whether it will last.

Some of the federal courts moved to the right when Donald Trump was president and Republicans controlled the U.S. Senate, which confirms judicial nominees. Trump appointed 54 judges to the circuit courts, which are one step below the U.S. Supreme Court, including filling one seat twice. That represents nearly 30% of the seats on the circuit courts, where cases are most often considered by three-judge panels.

Trump’s appointees flipped the 11th Circuit in the South to Republican control and expanded the GOP-appointed majorities in the 5th, 6th and 8th Circuits in the Midwest and South. Biden’s three appointees switched the New York-based 2nd Circuit to Democratic control.

Republican state attorneys general and conservative groups mostly filed their challenges in circuit courts dominated by conservative judges, while the unions went to circuits with more judges nominated by Democratic presidents.

In all, 34 objections have been filed in all 11 regional circuits plus the one for the District of Columbia. That’s where the ping-pong balls come in.

Under an arcane section of federal law, cases challenging federal agency actions get consolidated upon the agency’s request if they are filed in multiple circuit courts. Each circuit where a challenge is filed within the first 10 days of the agency taking action has an equal chance of being selected.

The staff at the Washington office of the Judicial Panel on Multidistrict Litigation pulls a ball out of a bin to determine where the case will be handled. No judges are involved in the drawings.

The U.S. Department of Justice has said in court filings that it expects the drawing to be conducted Tuesday.

The office denied a request by The Associated Press to allow media access to the drawing.

So far this year, the lottery has been used to assign just two cases. One involved fallout from a National Labor Relations Board ruling on an anti-union Twitter message by Tesla founder Elon Musk where objectors filed in two circuits. The other was over orders from the Federal Energy Regulatory Commission in which objectors filed in three.

The employer vaccine mandate is higher profile and further reaching. It calls for businesses with more than 100 workers to require employees to be vaccinated by Jan. 4 or wear masks and be tested weekly for COVID-19. Exemptions are provided for religious reasons and for those who work at home or only outdoors.

Because it’s an unusual rule from the workplace safety agency, there is no consensus among lawyers on how the challenges will go. OSHA has issued just 10 emergency rules in the half century since it was formed. Of the six challenged in court, only one survived intact.

The Biden administration has insisted it’s on strong legal footing. It also has the backing of the American Medical Association, which filed papers in support of the mandate.

“The AMA’s extensive review of the medical literature demonstrates that COVID-19 vaccines authorized or approved by FDA are safe and effective, and the widespread use of those vaccines is the best way to keep COVID-19 from spreading within workplaces,” the group said in its filing.

Among those challenging the rule is a consortium of construction contractors. They say they want their workers vaccinated, but that a requirement only on larger companies is just pushing vaccine-hesitant workers to take jobs with companies that have fewer than 100 employees.

“Crafting an unworkable rule that will do little to get construction workers vaccinated is an approach that is not only wrong, but likely counterproductive,” said Scott Casabona, president of Signatory Wall and Ceiling Contractors Alliance.

Officials with the workplace safety agency say they’re considering extending the mandate to smaller employers.

A three-judge panel of the 5th Circuit extended the stay of the OSHA rule in an opinion released last Friday, expressing skepticism.

“Rather than a delicately handled scalpel, the Mandate is a one-size fits-all sledgehammer that makes hardly any attempt to account for differences in workplaces (and workers) that have more than a little bearing on workers’ varying degrees of susceptibility to the supposedly ‘grave danger’ the Mandate purports to address,” wrote Judge Kurt Englehardt, a Trump appointee.

If that circuit does not keep the case after the lottery, the court that gets it could modify, revoke or extend the stay.

In its own filings, the U.S. Department of Justice said the federal courts do not need to decide so quickly whether to pause a rule that doesn’t go into effect until after the first of the year.

Sean Marotta, a Washington-based lawyer who has become an authority on using the lottery to assign cases, said he believes the judges who take action on cases before they have been consolidated are trying to leave their mark. Even if circuit court decisions won’t be the final word, they could serve as guideposts for the nation’s top court.

“This is most likely going to end up before the Supreme Court,” he said. “Judges might want to express a view that the Supreme Court might find persuasive.”

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Mulvihill reported from Cherry Hill, New Jersey. Associated Press writer Mark Sherman in Washington, D.C., contributed to this article.