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While the NBA Players Association’s executive committee is strongly against accepting the league’s recent “ultimatum” offer, it is not a certainty that the player reps who will meet with them 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 for 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 cancelled,” said Parker. “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 the 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.