Tom Brenner/Getty ImagesBy DEVIN DWYER, ABC News

(WASHINGTON) -- With Justice Ruth Bader Ginsburg dialing in from a hospital room, the U.S. Supreme Court on Wednesday heard arguments over the Affordable Care Act's contraceptive coverage mandate and whether the Trump administration can categorically exempt any organization that raises moral or religious objections.

The hearing -- which was conducted by teleconference and livestreamed to the public in an extraordinary arrangement prompted by the pandemic -- came a day after Ginsburg, 87, was abruptly admitted to the hospital for a gallbladder condition that had caused an infection.

Ginsburg participated actively in Wednesday's proceeding from the start, voicing concerns with the administration's sweeping rule that would allow more U.S. employers to opt-out of contraceptive benefits for women. She was discharged from the hospital later in the day, according to a statement from the court.

Millions of women obtain birth control at no cost through their employer-sponsored health insurance plans. The Department of Health and Human Services estimates that between 70,500 and 126,400 women could lose access to those services in one year if the Trump administration exemption is upheld.

"This leaves women to hunt for other government programs that might cover them," Ginsburg said, "which is exactly what Congress didn't want to happen."

The ACA, enacted in 2010, requires insurers to include "preventive care and screenings" as part of "minimal essential coverage," leaving it up to HHS to define what services qualify. All FDA-approved female contraceptives were included under the initial guidelines.

Houses of worship have always been exempt from having to include contraceptive coverage in their health plans for employees. But religious nonprofits and some independent businesses have contested the rule and subsequent government attempts to accommodate their concerns.

"Access to contraception is widely available in this country through many other means," said Solicitor General Noel Francisco, defending the administration's rules.

In a 2014 decision, the Supreme Court ruled that "closely held for-profit businesses" cannot be required to provide contraceptive coverage over their religious objections. The case did not address attempts at a compromise approach.

The Obama administration sought to accommodate companies with objections to formally register them with HHS, which in turn would trigger a system by which insurance companies would directly provide contraceptive benefits to women outside the employer's health plan.

Some groups said even the act of having to register their objection made them complicit, in violation of religious or moral beliefs.

"The problem is neither side wants the accommodation to work," said Chief Justice John Roberts addressing attorney Paul Clement, representing the Little Sisters of the Poor, an order of Roman Catholic nuns that's party to the case. "Is it really the case that there's no way to resolve those differences?"

"I don't think there really is a mechanism to find some third way because the government has always insisted on 'seamless coverage,' which means through the Little Sisters' (health insurance) plans," Clement said.

The Trump administration's rule is currently on hold under a nationwide injunction issued by lower federal court.

"These rules would allow, for the first time, publicly traded companies to claim the exemption," said attorney Michael Fischer, representing the state of Pennsylvania in challenging the Trump policy. "They advance an interpretation of the ACA that's inconsistent with its text and purpose."

Ginsburg is expected to remain in the hospital for a day or two. A Supreme Court spokeswoman said the other justices remain in good health during the pandemic. None are believed to have been tested for COVID-19.

The court is expected to deliver a decision in the ACA contraceptive coverage case by the end of June.

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