The arguments will last less than an hour. Brody is unlikely to rule for weeks, if not months, and her judgment will almost certainly be appealed.
Still, the hearing marks the first courtroom showdown since the suit was consolidated in Philadelphia last year. Its outcome could redraw the case, and with it the front lines of an issue in sports at all levels.
"It's a huge hurdle," said Stephen F. Ross, director of the Penn State Institute for Sports Law. If the NFL prevails, he said, then the process goes behind closed doors, into the world of labor arbitration.
There would be no public airing of evidence or testimony, and no higher court to review the decision. By contrast, a civil trial could open a window into confidential NFL files to show when league officials first sensed the dangers of concussions - and what they did about it.
With billions of dollars at stake, both sides have drafted courtroom all-stars. Former U.S. Solicitor General Paul Clement will argue on behalf of the NFL. The plaintiffs will be represented by David Frederick, a former assistant to the U.S. solicitor general who has argued 30 times before the U.S. Supreme Court.
The lawyers have declined to publicly comment before the hearing, which will include a second set of arguments on whether players' claims against helmet manufacturers should be litigated separately. But their battle is spelled out in court filings.
The NFL maintains the case is a labor dispute governed by the collective bargaining agreements that players and team owners have painstakingly negotiated for decades.
Those agreements, it contends, included provisions addressing players' injuries and care. They also say the contracts make clear that individual clubs and their medical staffs are responsible for diagnosing injuries and determining if or when a player returns to the field.
"Although the CBAs have changed over time pursuant to the collective bargaining process, every CBA expressly addresses player health and safety and provides grievance procedures for the resolution of disputes," NFL lawyers wrote in their 29-page brief to the judge.
Moreover, league lawyers argue that well-settled labor law dictates that disputes over contract interpretations must go to arbitration, not to a judge.
They cite multiple court decisions in which players' claims were dismissed because of the same "preemption" rule, including one last year by an Illinois judge in a wrongful-death case brought against the NFL by the estate of Dave Duerson, a former Chicago Bears safety.
Duerson's 2011 suicide - and a note in which he asked that his brain be donated for research - intensified the national spotlight on the issue of football concussions. His family has since joined the litigation.
The players contend that the NFL is a separate entity from the clubs, with different interests, including its singular role as a "responsible steward" for football.
"The NFL alone had the capacity to address football-related head injuries at a systemic level," their brief argues. "Only the NFL had the requisite access to data, credibility with players and broad influence necessary to achieve meaningful reform."
Their claims can't be subject to contract interpretation, they say, because the contracts were never intended to address fraud by the league and a "disinformation campaign to conceal the resulting brain injuries."
They also noted that the players and league operated without a collective bargaining agreement before 1968 and between 1987 and 1993, so players from those eras had no recourse in arbitration.
Andrew Brandt saw both perspectives. A lawyer, Brandt worked as a players' agent before spending a decade in the front office of the Green Bay Packers.
During his tenure there, Brandt said, the line between the league as an entity and the team owners wasn't always clear.
League officials occasionally inquired about an injured player's status, but teams acted independently when it came to decisions regarding players' health, he said.
"From a business point of view, we obviously look at the league as the stamp of approval," said Brandt, who left the Packers in 2008 and last year became director of the Jeffrey S. Moorad Center for Sports Law at Villanova University. "From a competitive point of view - the point of view of player decisions - everything was about the team."
Brandt said former players have asked him whether or not they should join the litigation. Some say they don't have symptoms of brain damage, but have been told joining the case costs nothing and might help provide them benefits if problems emerge later.
Brandt hasn't taken a position in the case, but said he cautions players who have no obvious health problems against getting in line for what he called "a money grab." As a lawyer, he also sees an uphill legal battle.
"No two concussions are alike - they are like snowflakes," Brandt said. "How do you deal with 4,000 players that have different issues?"
If Judge Brody allows the suit to proceed, the NFL is expected to mount other challenges to dismiss the case or whittle the prospective class.
League lawyers have signaled they will argue that the statute of limitations has expired against many of the claims. They also could demand that the aggrieved players - most who had played competitive football since they were boys - pinpoint a specific injury that led to their medical problems.
For now, the list of potential plaintiffs grows by the week. Last month, the family of former linebacker Junior Seau joined the case. Seau, a perennial Pro Bowl choice and likely Hall of Fame inductee, committed suicide last May at age 43.
Doctors later found evidence that he suffered from chronic traumatic encephalopathy, the brain damage linked to concussions. Duerson showed the same signs.
So did Tom McHale, who played offensive line for the Eagles in the 1990s and whose wife plans to attend Tuesday's hearing.
After leaving football, McHale turned to painkillers to offset chronic joint pain, and plunged deeper into depression and drug abuse. He died in 2008 after an accidental overdose of cocaine and OxyContin.
"I want nothing more than to prevent what happened to my husband to happen to other players in the future and their families," said Lisa McHale, who now works as an advocate and liaison for relatives of other players.
She watched her husband play football since both were in college and neither considered head trauma as a cause for his troubles. He never was diagnosed with a concussion.
But she has since come to believe that her husband was like many players, and either ignored, or was told to ignore, symptoms of head trauma. McHale said she believes the suit has already forced the league to confront the issue more quickly.
Ross, the Penn State law professor, agreed the public-relations aspect of the case - such as a barrage of images and stories of debilitated former players - could speed a resolution.
Regardless of how the hearing goes, he predicts an eventual settlement. Still, he said, "You'd always rather knock something out of the box early on."
Contact John P. Martin
at 215-925-2649, at firstname.lastname@example.org, or @JPMartinInky on Twitter.