Lawyers set to argue Tuesday's big health care cases were busy yesterday going through their final preparations in advance of oral arguments before the Fourth Circuit U.S. Court of Appeals in Richmond, Va.

Fox News spotted acting Solicitor General Neal Katyal checking out the large courtroom Monday morning while getting comfortable with the new surroundings. Folks around the courthouse call it the "green courtroom" because of the pool table-like color of the carpeting.

In an interview with FOX News, Virginia Attorney General Ken Cuccinelli said he had just spent the past 90 minutes with lawyers from his office going over courtroom strategy.

For all of their preparations, the lawyers still don't know what three judges will hear their case. Following the standard practices of the Fourth Circuit, the judges were randomly selected a couple of months ago but won't be publicly known until just after the courthouse opens at 7:30 Tuesday morning.

There are 14 judges on the Fourth Circuit, which had for years been known as one of the most conservative federal courts in the country. Today, there's an even split of judges nominated by Republican and Democratic presidents-including four from President Obama.

At 9:30 a.m., Liberty University v. Geithner is scheduled for 40 minutes of arguments. The dean of Liberty's law school, Mathew Staver will explain why he thinks the 2010 health care law's individual and employer mandates violate the Constitution. He will also argue that the law infringes on religious freedoms.

Katyal, in what may be his last high-profile act in the solicitor general's office, will defend District Court Judge Norman Moon's November 2010 decision against the school.

Then in an about-face, Katyal in the next case, Virginia v. Sebelius, will explain why the ruling of District Court Judge Henry Hudson, invalidating the so-called individual mandate, was wrong.

This case is also slotted to go 40 minutes but the judges may decide to extend argument time. Virginia Solicitor General Duncan Getchell will handle the duties on behalf of Cuccinelli and the commonwealth. Cuccinelli is expected to hold a news conference shortly after the courtroom adjourns.

The Fourth Circuit is well-known for its speedy proceedings. Dubbed the "rocket docket" it's no surprise that these health care challenges are the first in the country to reach an appellate courtroom. Rulings should come in the next couple of months and will likely put them at the head of the line for consideration by the Supreme Court.

Virginia's lawyers say there's a "palpable consensus" that the constitutionality of the health care law will ultimately be decided by the nine justices. If so, it's not clear by which case or cases they'll take as the vehicle for passing judgment.

The Fourth Circuit sits in the Lewis F. Powell Jr. Courthouse across the street from the Virginia statehouse. Powell, a native Virginian, was nominated to the Supreme Court by President Richard Nixon in 1971. He served on the high court until his retirement in 1987.

According to a history posted on the Fourth Circuit's website, the courthouse is the oldest in the federal court system. It was built shortly before the Civil War and housed key Confederate offices during the conflict. Afterwards, a grand jury indicted Jefferson Davis for treason but the case was never brought to trial.