NEW YORK -- As commissioner David Stern's deadline passed, the NBA and its players continued negotiating Wednesday in an attempt to end the lockout.

The two sides met for more than 11 hours to try to hash out a deal to save the season. The meeting got under way at 1 p.m. ET in New York, sources told ESPN The Magazine's Chris Broussard.

Stern had issued an ultimatum to players: Accept the league's latest proposal by 5 p.m. ET Wednesday or it will be replaced with a much harsher one that would drive the sides even farther apart.

Players said Tuesday they wouldn't accept the current one as configured and suggested another negotiation session.

The current offer calls for players to receive between 49 percent and 51 percent of basketball-related income, though union officials said it would be impossible to get above 50.2 percent. Players were guaranteed 57 percent of BRI under the previous collective bargaining agreement.

The next proposal would call for a 53-47 revenue split in the owners' favor, essentially a hard salary cap and salary rollbacks, which the league originally sought but had taken off the table. Both proposals were sent to union executive director Billy Hunter on Sunday.

The meeting featuring small groups from both sides was arranged Wednesday morning.

Failure to make a deal likely would increase the calls for the union to decertify so the players can file a lawsuit against the league in court, a risky and lengthy tactic that likely would doom the 2011-12 season. Union officials have downplayed the idea, but players might have no other leverage once the more severe proposal is put into play.

Stern and deputy commissioner Adam Silver were joined Wednesday by Spurs owner Peter Holt, the chairman of the labor relations committee, and lawyers Rick Buchanan and Dan Rube. Besides union executive director Billy Hunter and president Derek Fisher, vice presidents Roger Mason Jr. and Maurice Evans, economist Kevin Murphy and attorney Jeffrey Kessler represented the union.

Kessler took part just hours after saying he regretted telling the Washington Post that owners are treating players like "plantation workers" during the ongoing lockout. He said he planned to call Stern and apologize.

Flanked by the player representatives from 29 teams and roughly 15 more players who showed up for Tuesday's union meeting in New York, Hunter and Fisher announced that the player reps backed their recommendation to reject the NBA's offer made last weekend.

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.

Players indicated after their meeting Tuesday that they would be open to reducing their BRI take if owners made some changes on the system issues. Players offered to go to about 51 percent Saturday, with 1 percent going into a fund for retired player benefits.

But the league has placed as much importance on the system as the split, making it difficult to find compromise on the handful of items that remain unsettled. Owners believe there won't be the competitive balance they desire until payrolls are more equally balanced.

A month of games already has been canceled. Hunter said Tuesday he had heard Stern also planned to cancel games through Christmas without a deal Wednesday, though Stern later told NBA TV that "we have made no such plans, and we have had no such discussions."

Information from ESPN The Magazine's Chris Broussard, ESPN.com senior NBA writer Marc Stein, ESPN The Magazine's Ric Bucher, ESPN.com's Brian Windhorst and The Associated Press contributed to this report.