One of the most controversial provisions of ObamaCare -- the mandate requiring employers to cover contraception -- was debated before the Supreme Court on Tuesday, as activists on both sides of the issue clashed outside the courtroom in Washington.

The justices appeared divided in the case, which is the highest-profile challenge to the health care law since the Supreme Court narrowly upheld the Affordable Care Act in 2012.

The case argued Tuesday involves family-owned companies, including Hobby Lobby, that provide health insurance to their employees, but object to covering certain methods of birth control that they say can work after conception, in violation of their religious beliefs.

But the Obama administration and its supporters say a Supreme Court ruling in favor of the businesses could also undermine laws governing immunizations, Social Security taxes and minimum wages.

The outcome could turn on the views of Justice Anthony Kennedy, often the decisive vote. Kennedy voiced concerns both about the rights of female employees and the business owners. Kennedy asked what rights would women have if their employers ordered them to wear burkas, a full-length robe commonly worn by conservative Islamic women.

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Later in the 90-minute argument, he seemed troubled about how the logic of the government's argument would apply to abortions. "A profit corporation could be forced in principle to pay for abortions," Kennedy said. "Your reasoning would permit it."

Major advocacy groups attended the hearing and staged press conferences and demonstrations outside. On one side of the debate, Planned Parenthood and the American Civil Liberties Union argued that the rights of women should not be trumped by CEOs.

On the other side, Tea Party and other conservative groups and lawmakers argued that businesses should be free to choose whether they want to comply with this part of the law.

"This is about whether the federal government is forcing people to violate their own faith," Sen. Ted Cruz, R-Texas, said.

The Affordable Care Act requires employers to offer health plans with a range of services at no extra charge, including all forms of birth control for women that have been approved by federal regulators.

Some of the nearly 50 businesses that have sued over covering contraceptives object to paying for all forms of birth control. But the companies involved in the high court case are willing to cover most methods of contraception, as long as they can exclude drugs or devices that the government says may work after an egg has been fertilized.

The largest company among them, Hobby Lobby Stores Inc., and the Green family that owns it, say their "religious beliefs prohibit them from providing health coverage for contraceptive drugs and devices that end human life after conception."

Oklahoma City-based Hobby Lobby has more than 15,000 full-time employees in more than 600 crafts stores in 41 states. The Greens are evangelical Christians who also own Mardel, a Christian bookstore chain.

Last month, the Becket Fund for Religious Freedom, which is representing Hobby Lobby, filed a Supreme Court brief calling the mandate "one of the most straightforward violations … this Court is likely to see of a 1993 law preserving the free exercise of faith."

The other company is Conestoga Wood Specialties Corp. of East Earl, Pa., owned by a Mennonite family and employing 950 people in making wood cabinets.

The administration says a victory for the companies would prevent women who work for them from making decisions about birth control based on what's best for their health, not whether they can afford it. The government's supporters point to research showing that nearly one-third of women would change their contraceptive if cost were not an issue; a very effective means of birth control, the intrauterine device, can cost up to $1,000.

"Women already have an income gap. If these companies prevail, they'll have a health insurance gap, too," said Marcia Greenberger, co-president of the National Women's Law Center.

The contraceptives at issue before the court are the emergency contraceptives Plan B and ella, and two IUDs.

The government also argues that employers would be able to invoke religious objections under the 1993 Religious Freedom Restoration Act to opt out of other laws, including those governing immunizations, minimum wages and Social Security taxes. The Supreme Court previously has rejected some of these claims in cases decided before the law's enactment.

The issue is largely confined to family-controlled businesses with a small number of shareholders.

A survey by the Kaiser Family Foundation found 85 percent of large American employers already had offered such coverage before the health care law required it. There are separate lawsuits challenging the contraception provision from religiously affiliated hospitals, colleges and charities.

The federal appeals court in Denver ruled in favor of Hobby Lobby. Conestoga Wood lost its case at the federal appeals court in Philadelphia

Last month, a group of Democratic senators filed an amicus brief supporting the Obama administration's position in the case. A brief was subsequently filed on behalf of Hobby Lobby by Sens. David Vitter Ted Cruz, R-Texas; John Cornyn, R-Texas; and Mike Lee, R-Utah.

One key issue before the justices is whether profit-making corporations may assert religious beliefs under the 1993 religious freedom law or the First Amendment provision guaranteeing Americans the right to believe and worship as they choose. The court could skirt that issue by finding that the individuals who own the businesses have the right to object.

The justices still would have to decide whether the birth control requirement really impinges on religious freedom, and if so, whether the government makes a persuasive case that the policy is important and is put in place in the least objectionable way possible.

Hobby Lobby and Conestoga Wood say the burden they face is clear in the $100-a-day fine they would have to pay for each employee for not complying with the contraception provision. By contrast, businesses that choose not to offer health insurance at all can pay a tax of $2,000 a year for each employee.

But Mark Rienzi, a Catholic University professor who is on the Hobby Lobby legal team, said Hobby Lobby would be at a competitive disadvantage with other employers who offer health insurance. "Their view is and has always been that they want to take really good care of their employees and their families," Rienzi said.

The Associated Press contributed to this report.