David Boies, who joined the players in a legal claim against the owners, said they have filed an antitrust complaint in Northern District of California.
The district has a history of moving cases quickly.
Boies says the case is based on a boycott of NBA teams, which is a per se violation of antitrust laws. The only question is to whether the NBA has a labor exemption.
Amongst the plaintiffs in the lawsuit are Carmelo Anthony, Chauncey Billups, Kevin Durant, Leon Powe and Kawhi Leonard.
The ultimatum offer from David Stern is quoted in the complaint.
"That's not collective bargaining," said Boies.
Boies said that it is possible to get summary judgement before the season is canceled, but their goal is to resolve it out of court. Settlement negotiations can occur at any time and "might be a pathway by which an agreement could be reached," said Boies.
Boies was asked if Stern made a mistake.
"It turned out to be a mistake. Was it a mistake to do it? ... If you're in a poker game and you bluff, and the bluff works, you're a hero. If somebody calls your bluff, you lose."