By Stephanie Condon

The women of the Supreme Court and the conservative men on the court appeared split Tuesday over whether for-profit companies have religious freedom protections that would exempt them from providing their workers with health care coverage for contraception.

The justices listened to arguments from two privately-held, for-profit companies — Hobby Lobby Stores, Inc. and Conestoga Wood Specialties Corp. The companies have sued the government over the Obamacare mandate requiring companies with more than 50 employees to provide comprehensive health coverage (including contraception) or pay a fine.

The case encompasses some of the most politically divisive themes and issues of the 2012 election — Obamacare, the left’s “war on religion,” the right’s “war on women,” and the notion of corporate personhood. It also has far-reaching implications. If Hobby Lobby and Conestoga prevail, it would prompt “a fundamental shift in the understanding of the First Amendment,” David Gans, the civil rights director for the Constitutional Accountability Center, told CBS News.

A ruling in favor of Hobby Lobby or Conestoga would give for-profit companies unprecedented protections under the First Amendment. The Obama administration already exempts nonprofits with religious affiliations, such as Catholic universities, from the contraception coverage rule.

The Supreme Court’s three female members on Tuesday led the charge to defend the Obamacare mandate, CBS News’ Jan Crawford reports. Echoing arguments put forward by the Obama administration, Justices Elena Kagan and Sonia Sotomayor both asked how a ruling in favor of Hobby Lobby would affect an employer who may object to blood transfusions on religious grounds, or vaccines — or any other sort of health care that’s part of a comprehensive care package.

The court’s conservative justices, meanwhile, seemed sympathetic to arguments that business owners with deeply-held religious beliefs should not be forced to pay for health care treatments they object to, Crawford reports.

Hobby Lobby is arguing that it has religious expression freedoms under the Religious Freedom Restoration Act, which dictates that an individual’s religious expression shouldn’t be “substantially burdened” by a law unless there is a “compelling government interest.”

Even if Hobby Lobby were protected under that law, Kagan said that it’s dubious that Hobby Lobby faces a “substantial burden,” given that company could simply pay the fine rather than provide their employees with insurance. Their employees could then acquire insurance on the new Obamacare marketplaces.

Justice Antonin Scalia, however, sided with Hobby Lobby’s lawyers. They argued that it would be an onerous burden for the company to pay a fine and then pay the higher wages it would feel compelled to pay its employees to make up for lost benefits.