WASHINGTON -- Justices on the Supreme Court seemed to struggle Tuesday with the question of whether a private company can get out of a federal law by citing the religious beliefs of its shareholders.

Hobby Lobby Stores, Inc., a Christian-owned crafts supply chain, and Conestoga Wood Specialties Corp., owned by Mennonite Christians, are challenging the provision of the Affordable Care Act that requires for-profit companies to include all Food and Drug Administration-approved contraceptives in their health insurance plans.

Hobby Lobby's attorneys argue that the law violates the company's constitutional right to religious freedom by forcing it to cover all forms of birth control or pay steep fines. The company's owners are morally opposed to intrauterine devices and emergency contraception, believing it to be a form of abortion, though medical studies have debunked that claim.

The contraception mandate does include exceptions for churches and a special accommodation for religiously affiliated nonprofits, such as schools and hospitals. But for-profit corporations are required to cover the full range of women's preventative care, including birth control, intrauterine devices and emergency contraception, at no cost to their female employees.

At oral arguments on Tuesday, the women justices were the most aggressive in their questioning of Hobby Lobby's lawyer, former Solicitor General Paul D. Clement. Justices Sonia Sotomayor and Elena Kagan asked whether other companies should be allowed to refuse to cover other procedures, like blood transfusions and vaccines, if employers had a religious objection to such medical treatments.

"There are quite a number of medical treatments that could be religiously objected to," Kagan stated. "Everything would be piecemeal, nothing would be uniform."

Kagan also suggested that corporations could challenge other federal laws, like minimum wage and family leave requirements and protections against child labor, based on their religious beliefs.

But Clement said such a "parade of horribles" would not actually come before a court, and no company had challenged a minimum wage law, for example, based on religious considerations.

Justice Anthony Kennedy, who many expect to be the swing vote in this case, questioned both sides aggressively. Kennedy asked Clement why the company couldn't just choose not to provide health insurance at all, pay a tax and then raise salaries to allow employees to purchase health care on their own. Assuming that would be a financial "wash," Kennedy asked Clement, "Then what would your case be?"

"How would we consider the rights of employees?" Kennedy asked. "The employees may not believe … in the religious beliefs of the employer."

Justice Antonin Scalia alternatively asked why the government couldn't simply pay for the "three or four" kinds of birth control that some religious employers consider to be "abortifacients" -- namely, the morning-after pill and intrauterine devices. "That's not terribly expensive, is it?" he asked.

The administration's attorney, Solicitor General Donald Verrilli Jr., said federal and state laws "don't consider these particular forms of contraception to be abortion." He said the government respected different beliefs on the subject, but noted that the some 2 million women who take those forms of birth control don't believe they are "engaged in abortion."

Kennedy also questioned Verrilli as to why the Department of Health and Human Services had granted accommodations on the contraception coverage rule -- but not other parts of the Affordable Care Act -- to religiously affiliated nonprofits if the government had a compelling interest in providing birth control coverage to all women.

"It must have been because the health care coverage was not that important," Kennedy said.

Some justices also asked whether for-profit corporations had the right to claim religious freedom exemptions to any federal laws.

"How does a corporation exercise religion?" Sotomayor asked.

Justice Samuel Alito proposed a hypothetical of whether a Jewish or Muslim butcher would be able to provide kosher or halal meats, if the butcher's shop was formed as a corporation and Congress outlawed such techniques as a form of animal cruelty.

Verrilli said that in that case, individual customers would have standing to challenge the law, and the butcher might be able to step in in order to argue on their behalf.

Justice Ruth Bader Ginsburg said it would have been "strange" for a large bipartisan part of Congress to pass a piece of legislation, the Religious Freedom Restoration Act, if they believed it would allow for-profit companies to be exempt from federal laws because of the religious beliefs of their shareholders. She pointed out that an amendment along those lines was rejected by the Senate.

If Hobby Lobby wins and the Supreme Court eventually rules that companies have a right to exercise religious freedom that exempts them from complying with federal law, the decision could have a far-reaching impact beyond women's health. For instance, such a ruling could open the door to more controversial laws like Arizona's recently debated "religious freedom" bill, which would allow businesses to refuse to serve LGBT people.

As Kagan suggested Tuesday and as Verrilli wrote in a brief he filed on the case this month, the ruling also has the potential to get businesses out of having to comply with minimum wage and hiring discrimination laws, Social Security taxes and vaccination requirements.

"Allowing a corporation, through either shareholder vote or board resolution, to take on and assert the religious beliefs of its shareholders in order to avoid having to comply with a generally-applicable law with a secular purpose is fundamentally at odds with the entire concept of incorporation," Verrilli argued in the brief.

This time around, Kennedy potentially could return to his common role as the court's swing vote. Kennedy wrote the broad opinion in the Citizens United case, which found that the First Amendment prevented the government from limiting independent expenditures by corporations, but he's also been one of the court's strongest voices for gay rights, which could be negatively impacted if Hobby Lobby gets its way.

Read the full transcript below: