While the National Basketball Players Association's executive committee is staunchly against accepting the league's recent "ultimatum" offer, it is not a certainty that the player reps who will meet with it Tuesday will feel the same way, a source close to the situation told ESPN The Magazine's Chris Broussard on Monday.
The source said some of the reps may favor decertification, while others may want to accept the deal.
"I don't think there's going to be a consensus," the source said. "And that would be a problem."
Anthony Parker, the representative for the Cleveland Cavaliers, said he is in favor of rejecting the league's offer, while one player rep who did not want to be identified told ESPN.com that he is leaning toward voting to accept the deal.
"Most of the people I'm talking with don't like the deal," Parker said. "We don't think it's a good deal for the players."
Parker said he realizes that if the players reject the deal, decertification may be their only option.
"Being for decertification does not mean you want the season to be canceled," Parker said. "Even if we decertify there will still be plenty of time to get a deal done and that's our hope."
With a Wednesday deadline looming to accept the league's latest labor proposal, player representatives from all 30 teams have been summoned by the union to New York for the mandatory meeting to update them on negotiations, sources have told ESPN.com.
Union sources have said the executive board remains unwilling to present that offer to the union's estimated 450 members for a vote and plans to make that stance clear to team player reps at the meeting.
Sources told ESPN.com that union leaders have not budged from the view that the NBA's offer is "unacceptable," just as NBPA president Derek Fisher described it in the wee hours of Sunday morning once Saturday's marathon bargaining session finally ended.
On Monday, meanwhile, sources say that players and agents backing the decertification of the union have scheduled another conference call to follow the two conference calls -- each with at least 50 players dialed in -- that took place last week.
The players association's executive board also was set to conduct a conference call Monday to discuss its options before Tuesday's meeting, Spurs forward Matt Bonner, a committee member, told the San Antonio Express-News.
No new negotiations are scheduled after the parties spent nearly nine hours negotiating under the auspices of federal mediator George Cohen. NBA commissioner David Stern emerged from those talks saying that the union had until the end of business Wednesday to take a deal that the league says will pay players up to 51 percent of annual basketball-related income or prepare to brace itself to receive an offer that tops out at 47 percent of BRI and features the more restrictive flex cap that the players emphatically shot down in June.
"We hope that this juxtaposition will cause the union to assess its position and accept the deal," Stern said at a news conference early Sunday morning.
There is no evidence in circulation yet to suggest that more than a handful of rank-and-file players are lobbying the union to put Saturday's offer from the owners to a vote.
In an interview with ESPN on Monday, Stern downplayed the threat of decertification of the union, an option that could be more strongly considered if the backup proposal gets put on the table. A lengthy court fight almost certainly would wipe out the entire 2011-12 season.
"The reality is that that decertification route, or something like it, was tried by the NFL players and the Court of Appeals for the Eighth Circuit soundly rejected the attempt," Stern said on "SportsCenter," referring to the NFL Players Association's decertification process during that league's summer labor dispute. "I just don't know what they're thinking."
A month of games already has been canceled.
"We're all really concerned. This is our livelihood. This is our job," Charlotte point guard D.J. Augustin said Monday after playing a pickup game with other NBA players in Houston. "For ourselves, we want to get back playing. But we're also not going to take just any deal. We're going to stay united, stay strong and just be ready whenever they call us back."
Though frustrations are high and nasty rhetoric remains -- the league and union briefly argued about their proposals through Twitter feeds Monday -- the reality is they've grown closer on paper. Players offered Saturday to reduce their BRI take to 51 percent, with 1 percent going to a fund for retired players' benefits, after previously saying they wouldn't go below 52.5.
The question is whether they can erase the remaining issues before Wednesday's deadline -- and what happens if they don't.
"We just want a fair deal, and I believe the players' union is just trying to get the fairest deal possible," Washington forward Rashard Lewis said. "They gave us a deadline on Wednesday, but our side is meeting today or tomorrow. So let's just see what happens."
Information from ESPN.com senior writer Marc Stein and The Associated Press was used in this report.