Even as Obamacare struggles in the court of public opinion, the new health care law will face another legal threat Tuesday when a group of small-business owners and others argue in federal court that they should be exempt from the tax credits and financial penalties created under the law.

Halbig v. Sebelius is one of four lawsuits challenging the Affordable Care Act, which plunged in popularity after a glitch-plagued debut on Oct. 1. Legal experts said a victory for the businessmen could seriously undercut the law.

"Of all the legal challenges to the law, this is the one that has the potential for blowing the whole thing up," Mike Tanner, a health care policy expert at the libertarian Cato Institute, told the Washington Examiner.

Arguments in the case are scheduled for 2 p.m. on Tuesday in the U.S. District Court for the District of Columbia.

The lawsuit challenges the legality of tax subsidies provided under the law to help people buy health insurance. It's being heard after U.S. District Judge Paul Friedman in October rejected the administration's request to throw out the case.

"He's at least indicated that the [business owners] have a case," Tanner said.

The business group claimed in its court filings that the Internal Revenue Service overstepped its authority under the law by providing federal subsidies in states that effectively rejected Obamacare by refusing to create the health insurance exchanges required by the law. Those states now should not have to abide by the law's mandates and penalties, the group argued.

"If an exchange was not established by a state, but by the federal government … no subsidies are available," wrote the business group and individuals from states that refused to create their own exchanges. The IRS ruling, they said, would further burden small businesses with heavy fines.

The lawsuit was brought by Innovare Health Advocates, a Missouri medical practice, and others. Jacqueline Halbig, of Alexandria, Va., a former Bush appointee who runs a consulting firm, also joined the suit. So did David Klemencic, a small-business owner from West Virginia.

Washington and Lee law professor Timothy Jost said a victory for the business group could accomplish something congressional Republicans have failed to achieve after dozens of attempts: It could torpedo Obamacare. Exempting people in the states covered by the lawsuit could undercut Obamacare's financial stability.

"Basically we are now at the first step, on the merits of the case," Jost said. "So this case has gotten through the front door, but I'm confident this court is going to throw this out."

The judge pledged to make a decision in 60 days or so, allowing the business group time to come into compliance with the law before Jan. 1.