Updated

A Virginia university is the latest party to request the Supreme Court step in and resolve the multifront legal brawl over the constitutionality of President Obama's health care overhaul.

Liberty University, a private Christian university founded by the late Jerry Falwell, asked on Monday for the high court to review an appeals court's decision to dismiss its challenge of the law.

The move comes after the Department of Justice and Virginia Attorney General Ken Cuccinelli each petitioned the Supreme Court to review the legality of the law. But in seeking to add their case to the list, Liberty University lawyers are trying to have the justices dig even deeper.

Whereas other suits hinged mostly on a challenge to the law's "individual mandate" -- the requirement that most Americans obtain health insurance coverage -- the Liberty University case also challenged similar requirements on employers to extend coverage to workers.

"We're the only case that actually raises the employer mandate," said Mathew Staver, lead lawyer on the case and founder of Liberty Counsel. The 4th Circuit Court of Appeals dismissed the case last month.

Staver told FoxNews.com he anticipates the Supreme Court, which began its term last week, will decide before the end of the year which cases it will hear, and schedule oral arguments for some time in early 2012. Staver said it's possible the court will take multiple cases, schedule them "back to back," and then potentially issue a joint opinion covering all the cases.

"You really want to dispose of everything at one time," he said.

Staver said it would be a "quantum leap" for the court to uphold the law.

But the Justice Department last month urged the Supreme Court to do just that, comparing it to longstanding and sweeping policies like the Civil Rights Act and Social Security Act which were ultimately upheld.

The Justice Department predicted challenges to the Affordable Care Act would similarly fizzle.

The Obama administration last month appealed a decision from the 11th Circuit Court of Appeals in Atlanta, which ruled against the law.

The 26 states that brought that challenge likewise requested Supreme Court intervention.

In the 4th Circuit case, Liberty University and two other private individuals are asking for a Supreme Court review.

Staver said the case is also unique because the decision of the appeals court hinged on a ruling that the individual mandate is a "tax" -- and that as such, the court could not rule on it until a taxpayer sought a refund of that tax. Staver argues that the requirement amounts to a penalty, and wants the Supreme Court to review that issue as well as the merits of their claim.

In the petition filed Monday, Liberty University described the dual mandates as "unprecedented."

The filing argued that it would require individuals to purchase a "vaguely defined and burdensome health insurance product," making a similar argument about the requirement on employers.

The mandates are not set to go into effect until 2014. On the employer end, the law would require some employers with more than 50 workers to offer coverage, imposing a fine on those that don't comply.