The NBA Players Association has rejected the league's latest labor proposal and asked for one more bargaining session before a 5 p.m. deadline Wednesday that, according to commissioner David Stern, will cause the offer to vanish if there's no agreement.

Flanked by the player representatives from 29 teams and roughly 15 more players who showed up for Tuesday's union meeting in New York, NBPA executive director Billy Hunter and president Derek Fisher announced that the player reps backed their recommendation to snub the NBA's offer from the weekend, which Stern says will be replaced by a far less appetizing offer if the sides can't reach an accord by the stated deadline.

"Our orders are clear," Fisher said. "The current offer that is on the table from the NBA is not one that we can accept."

Yet Hunter -- after sources confirmed to ESPN.com that the union, for the first time since the lockout began, is prepared to accept a 50/50 split of annual revenue -- expressed great confidence that the league and NBPA would resume negotiations one last time before Wednesday's buzzer.

Stern said in a subsequent interview on NBA TV on Tuesday night that he will take Hunter's call and consider the prospect of further bargaining before the deadline, but otherwise said little to suggest that his owners are prepared to budge on the five or so remaining "system" issues that still separate the sides even if the union is now amenable to a 50/50 split.

"I always take Billy's calls as a sign of respect and courtesy," Stern said. "What my response will be will be guided to some degree by the labor relations committee."

A meeting Wednesday between the sides is tentatively scheduled for 1 p.m. ET, sources told ESPN The Magazine's Chris Broussard. Logistics for the meeting currently are being worked out, including which hotel will host the talks.

Sources said that the union did not conduct a formal vote of the players assembled in the room Tuesday, opting instead for an informal "everyone agrees" consensus that authorizes Hunter and Fisher to accept a 50-50 split of basketball related income in future negotiations as long as the league makes some concessions on some of the remaining system issues. But sources briefed on the owners' thinking insisted to ESPN.com that there will be no further budging from the owners, no matter how close a deal seems on paper. Wednesday will be the 132nd day of the second lockout in NBA history to bleed into the regular season.

"It's sad," one ownership source said. "I think they've seen their best offer."

Hunter, though, is so convinced that the owners will indeed bend that he didn't hesitate to trumpet at Tuesday's news conference that he thinks the league's current proposal actually won't be yanked off the table after Stern's deadline.

"The players are clearly of the mind that it's an unacceptable proposal," Hunter said. "But because of their commitment to the game and their desire to play, they're saying to us that we want you to go back, see if you can go back, get a better deal."

Billy Hunter and the NBPA refused to accept the owners' take-it-or-leave-it labor proposal. Patrick McDermott/Getty Images

Said Cleveland Cavaliers player rep Anthony Parker: "Once the league's offer was spelled out clearly, everyone (in the room) said it was worse than they thought."

Sources said that the union did not conduct a formal vote of the players assembled in the room Tuesday, opting instead for an informal "everyone agrees" consensus that authorizes Hunter and Fisher to accept a 50-50 split of basketball related income in future negotiations as long as the league makes some concessions on some of the remaining system issues.

Fisher insisted that without the system concessions "we don't see a way of getting a deal done between now and end of business" Wednesday.

"We're open-minded about potential compromises on our [BRI] number," Fisher said. "But there are things in the system that are not up for discussion, that we have to have, in order to be able to get the season going again."

The league's weekend offer calls for players to receive between 49 percent and 51 percent of annual basketball-related income. Union officials argue that it would be nearly impossible for the league to generate sufficient revenue in any given season to earn the players more than 50.2 percent, but Hunter and Fisher now have the go-ahead for the first time all summer to go that low on BRI if the owners will agree to relax some of the various limits they want to impose on teams that stray into luxury-tax territory.

The tax penalties and other rules for tax-paying teams, one source told ESPN The Magazine's Ric Bucher, are where the two sides remain at complete odds.

A group of hard-line owners -- several of whom, according to a Tuesday report from Broussard, hope the players reject the current offer so they can push for a more restrictive financial system -- maintain that restrictions on tax-paying teams are the only way to stop big-market teams from hoarding the game's biggest stars and increase competitive balance in a league that has seen only nine franchises win championships over the past 31 seasons.

Sources told ESPN.com that player representatives attending Tuesday's meeting were apprised by union officials that the NBA would currently expect 16 teams -- 17 if you include the league-owned New Orleans Hornets -- to ratify the deal in its current form and 13 to oppose it.