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The effect that conservative Justice Antonin Scalia's death is having on the Supreme Court's most divisive issues will get another big test when the court convenes Wednesday in the battle pitting religious freedom and birth control.

The current eight-judge panel is set to hear its fourth Obamacare-related case, this time involving religiously affiliated nonprofits that are challenging a government provision requiring employers to include contraceptive coverage in their health care plans.

But with a court that's generally evenly divided along ideological lines, without Scalia, a 4-4 tie is entirely possible. That would leave the various lower court rulings in effect — an outcome the high court would rather avoid.

A tie would be especially problematic now because federal appeals courts that previously heard such cases were not in agreement on the issue. Three of the courts ruled for the government, but one ruled in favor of the religiously affiliated groups. A Supreme Court tie would leave that split in place.

That means women who work for the organizations would have direct access to contraceptive coverage in some states, but not in others.

Two years ago, when the Supreme Court ruled in the Hobby Lobby case that religiously oriented businesses could object to providing contraceptive coverage, the court was split 5-4 with Scalia in the majority.

About two dozen religiously affiliated schools, seminaries, hospitals and charities from around the nation have sought to legally oppose this particular contraceptive provision.

Protesters rally at the steps of the Supreme Court in March last year, as arguments began to challenge the Affordable Care Act's requirement that employers provide coverage for contraception as part of an employee's health care. LARRY DOWNING / Reuters

Houses of worship and their auxiliaries are completely exempt from the requirement. The religiously affiliated groups coming before the Supreme Court Wednesday say they should be as well.

The Obamacare law allows such organizations to opt out of directly providing contraceptive coverage. But those groups say the accommodation still makes them complicit in providing access to birth control and abortion, which violates their religious views.

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Among the challengers is an organization of Catholic nuns called The Little Sisters of the Poor, which operates 27 homes for the low-income elderly.

Related: Birth Control is Back at the Supreme Court

Paul Clement, a Washington, D.C., lawyer who will argue before the court on their behalf, says the law’s requirement “is literally as nonsensical as saying the priests are exempt but the nuns are not.”

An organization that objects on religious grounds to providing the coverage must notify the Department of Health and Human Services in writing and provide information about its health insurance plan. The government then notifies the insurer that it must assume the responsibility of providing contraceptive coverage at no cost to the beneficiaries.

But the groups argue that even that arms-length arrangement violates their religious freedom.

They don’t object to any government action that provides contraceptives to their employees, Clement said, “but they do object to being compelled to take government-prescribed actions to facilitate that coverage.”

Related: Yes, You Have to Pay for Birth Control, Feds Tell Insurers

Sister Constance Veit of the Little Sisters in D.C. acknowledges that under the accommodation, they would no longer be paying for contraceptive coverage.

"That’s never been the point with us," she told NBC News. "The services would still become a part of our health plan, and that’s just something we can’t agree to."

The eight justices must decide whether the government’s accommodation violates a federal law called the Religious Freedom Restoration Act. It forbids the government to impose a substantial burden on the exercise of religious beliefs, unless the challenged provision is the least restrictive way to satisfy a compelling government need.

It can’t be very compelling, the groups argue, given that the government has already allowed so many different types of exceptions that exempt employers of tens of millions of people — everyone from churches to for-profit companies founded on religious principles to employers whose health care plans were unchanged since the Affordable Care Act was signed into law by Obama in 2010.

The Obama administration argues that the challengers want not only to be relieved from the obligation of providing contraceptive coverage themselves but also to prevent the government from working with other entities to fill the gap.

Such a claim "stretches the Religious Freedom Act too far," said Solicitor General Donald Verrilli, in a brief submitted ahead of Wednesday’s courtroom argument.

The right to free exercise of religion does not include the right to restrict others from seeking the health care they need, he wrote, adding that "contraceptives are an essential component of women’s health care."

Once they file notice of their objection, the government takes over, invoking its independent authority to arrange for insurers or plan administrators to provide the coverage. It is not delivered through an entity owned or controlled by the employer, Verrilli said.

The challengers "may not use a religious objection to dictate the government’s control of its internal affairs," he added.

Related: What Hobby Lobby Ruling Means

If the challengers win, Verrilli argues, women would be forced to undertake extra steps to learn about and sign up for benefits through some other plan — thwarting one of the purposes of Obamacare to "ensure that women receive equal health coverage and to remove barriers to the use of preventative services.”

The case has attracted 70 friend-of-court briefs — even from 240 students, staff and faculty members of religiously affiliated universities that don't want women to lose access to birth control.

"Tens of millions of women nationwide depend on contraceptive coverage to prevent unintended pregnancies, treat serious medical problems, and ameliorate the resulting educational, professional, and medical harms,” one brief says.