A meeting Wednesday between the NBA's owners and its locked-out players got under way at 1 p.m. ET in New York, sources told ESPN The Magazine's Chris Broussard. The NBA Players Association rejected the league's latest labor proposal Tuesday but had asked for one more bargaining session before a 5 p.m. ET deadline Wednesday that, according to commissioner David Stern, will cause the offer to vanish if there's no agreement. Wednesday is the 132nd day of the second lockout in NBA history to bleed into the regular season. Flanked by the player representatives from 29 teams and roughly 15 more players who showed up for Tuesday's union meeting in New York, union executive director Billy Hunter and president Derek Fisher announced that the player reps backed their recommendation to reject the NBA's offer made last weekend. Stern says it will be replaced by a far less appetizing offer if the sides can't reach an accord by the stated deadline. 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 might appear on paper. The league's offer last weekend calls for players to receive between 49 percent and 51 percent of annual BRI. 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. Cleveland Cavaliers owner Dan Gilbert has been one of the faces of the so-called "hardline" owners during the protracted talks. He's long been one of the certified "hawks" -- the aggressive and hungry faction that was known to be seeking radical change. However, multiple sources have confirmed to ESPN.com that Gilbert has adjusted his position in recent days and moved into a more moderate mode, voting with fellow owners who are willing to accept a 50/50 share of BRI.