The union, which filed the motion Tuesday on behalf of New Orleans defensive end Will Smith, Cleveland linebacker Scott Fujita, and free agent defensive lineman Anthony Hargrove, argues the players will suffer irreparable harm if they are forced to miss games while their case against the league proceeds.
Suspended Saints linebacker Jonathan Vilma had already filed a similar motion when his full-season suspension began earlier. The other three players' suspensions began this week.
The players ultimately want their suspensions thrown out because they argue the disciplinary process was fundamentally flawed and unfair.
U.S. District Judge Ginger Berrigan, who is hearing the case, has said she found the league's handling of the bounty matter to be unfair to the players and their punishments excessive, but she has also said she is not yet comfortable that federal courts have jurisdiction to rule on a process that was collectively bargained between the union and the league.
She has already indicated, in response to Vilma's earlier request for a temporary restraining order, that she was inclined to wait until players had exhausted their remedies under the league's collective bargaining agreement before she ruled.
Still pending on that front is a decision by a three-member panel that last week heard arguments in the NFLPA's appeal of a system arbitrator Stephen Burbank's ruling that Commissioner Roger Goodell had the authority both to punish the players and hear their appeal in the bounty matter.
The union had argued that because actions alleged in the bounty matter happened on the field, the league's labour agreement calls for someone other than the commissioner to hear players' appeals of the commissioner's disciplinary action.
The three-member panel has indicated that it hoped to rule by this week. If it rules in favour of the players, Berrigan would have no reason to act.
The NFL has said its investigators have concluded that the Saints ran a bounty program from the 2009 through 2011 seasons. The league said the program offered improper cash bonuses to defensive players for hits that injured opponents.
The players have admitted to a pay-for-performance program for big plays such as turnovers and big, clean hits, which also is banned but cannot be punished by suspensions. However, they have denied, some under oath in federal court, that there was a pay-to-injure program.
In addition to the four players suspended, the league also suspended Saints head coach Sean Payton the entire season, Saints general manager Mickey Loomis for half the season, and Saints assistant head coach Joe Vitt for six games. Former Saints defensive co-ordinator Gregg Williams, who is now with St. Louis and allegedly administered the bounty pool, has been suspended indefinitely.Suggest a correction