NEW YORK -- Commissioner David Stern gave NBA players an offer and a deadline: Accept a chance to earn up to 51 percent of basketball-related income by Wednesday or get ready for a deal that's a whole lot worse.

He wouldn't call it an ultimatum, but it didn't sit well with the union.

"The players will not be intimidated," attorney Jeffrey Kessler said early Sunday after eight hours of negotiations stretched late into the night. "They want to play, they want a season, but they are not going to sacrifice the future of all NBA players under these types of threats of intimidation. It's not happening on Derek Fisher's watch; it's not happening on Billy Hunter's watch; it's not happening on the watch of this executive committee."

Kessler said the proposal was really 50.2 percent for the players and called the chance of them ever reaching 51 percent a "fraud" and an "illusion."

If players don't agree to it by Wednesday, Stern said they would get a deal that would guarantee them just 47 percent of BRI and call for a flex salary cap.

"We hope that this juxtaposition will cause the union to assess its position and accept the deal," Stern said.

Thus ended another frustrating day, one that puts a lengthy 2011-12 season in doubt.

"Today was another sad day for our fans, for arena workers, our parking lot attendants, our vendors. Very frustrating, sad day," union president Fisher added. "We, for sure, unequivocally, made good faith efforts to try to get this deal done tonight. And we're at a loss for why we could not close it out."

And it remains difficult to see how they can. Stern certainly wouldn't speculate on the chances.

"I'm not going to make percentage guesses or anything like that. We want our players to play. We'd like to have a season," he said. "These are the terms upon which we're prepared to gear up and get in as many games as possible."

Players and owners met with federal mediator George Cohen for more than eight hours, and Stern said Cohen offered six "what if?" recommendations relating to the BRI split and the salary cap system.

Stern said owners accepted the first five and would put them in writing in a formal proposal to the players, hopefully Sunday. But it wasn't acceptable Saturday, with Stern saying Kessler rejected it.

"I think it's fair to say that speaking on behalf of the union, Mr. Kessler rejected the mediators' recommendations and our proposal," Stern said. "But hope springs eternal, and we would love to see the union accept the proposal that is now on the table."

Though insistent on no more than a 50-50 split, owners will offer the players a band that would allow them to receive between 49 percent and 51 percent of revenue. However, Stern's description of how it would work was confusing, and Kessler said under "the wildest, most unimaginable, favorable projections and we might squeeze out to 50.2."

Fisher said the players' proposal would have given them about 51 percent, with a portion taken out to use for retired players' benefits.

The union on Sunday night took the step of summoning the player representatives from all 30 teams to New York for a mandatory meeting Tuesday to update them on labor talks, sources with knowledge of the Players Association's plans told ESPN.com's Marc Stein. It's believed to be the first time during the lockout that the union has insisted that each team's player rep attend or send an alternate to a meeting.

Day 128 of the lockout came at the end of a tenuous week in which both sides seemed as much at odds with themselves as each other. Some players took part in conference calls to discuss the option of decertifying the union and filing an antitrust case against the league, while hardline owners were in favor of offering the players 47 percent now and not going beyond 50.

Another conference call regarding the ins and outs of decertification is being scheduled for Monday, sources told ESPN.com's Marc Stein.

Two such conference calls, each with at least 50 players dialed in, took place last week, with Boston Celtics swingman Paul Pierce taking on a leadership role on both calls. One source close to the process told ESPN.com on Sunday that the players and agents pushing decertification ambitiously hope to secure as many as 200 signatures on the petition calling for the vote to ensure they go well past the required 130 signatures.

"We intend to move fast," one source said.

Once signatures are collected from 30 percent of the players, that petition is filed with the National Labor Relations Board. The NLRB could then take an estimated 45 days to verify the petition and schedule an actual decertification vote. Disbanding the union requires a simple majority of players voting for decertification, but the union would continue to exist while the NLRB is arranging the vote and thus could theoretically continue negotiations with the league before the Players Association is dissolved.

"I've been ready to sign a decertification petition since July?" Nets guard Deron Williams tweeted Saturday. "Can't believe we are just now going this route! SMH."

Decertification backers believe that the fear of the unknown once the union is decertified, with the labor fight then moving into courtrooms, would finally move NBA owners off the extreme hard-line negotiating stance they've maintained throughout the four-month lockout and lead to a more palatable offer during that 45-day window.

Sources on the ownership side, however, believe that the pre-emptive federal lawsuit filed by the NBA during the summer could potentially take the sting out of any potential decertification, although that remains a matter of some debate among legal analysts.

There is even stronger conviction on the ownership side in questioning whether a majority of players would indeed have the stomach to go through with full-on decertification, since that step would almost certainly seal the cancellation of the entire 2011-12 season and throws up as many unknowns for the players as it would for the owners. But the success of a decertification vote likely depends on its timing, since most experts agree that a vote would surely pass if the NBA cancels the season first.

Although Saturday's lengthy meeting offered hope of compromise -- despite the rare attendance of Hall of Famer and Charlotte owner Michael Jordan, and Portland billionaire owners Paul Allen, considered to be hard-liners -- Kessler said owners never really made any.

"They came in here with a prearranged plan to try to strong-arm the players," he said. "They knew today they were sticking to 50, essentially 50.2. They were going to make almost no movement on the system, and then they were going to say, 'My way, or the 47 percent highway."

He added there was no reason to talk again before Wednesday if the owners stick to their current position.

Other items in the new owners' proposal related to rules for teams paying the luxury tax and for the use of the midlevel exception. Players have said the system issues are just as important as the BRI split, because they fear owners' proposals essentially would prevent teams in the biggest markets from being free-agent options.

A month of the season already has been lost, and more games could be in jeopardy soon. Nobody said the decertification threat made any real impact on the discussions, but Fisher also said there's not a deal yet that's worth a vote.

If they can't agree to one by Wednesday, it will be even harder to find common ground. Players already rejected a flex cap in June.

Fisher and Kessler again questioned the owners' willingness to negotiate, but Stern said they were ready to make a deal -- by Wednesday.

"We want to allow the union enough time to consider our most recent proposal, and we are hopeful that they will accept," he said.

As for the Wednesday deadline, he added that it "doesn't aid the negotiating process to just leave it hanging out there."

Information from The Associated Press and ESPN.com senior writer Marc Stein was used in this report.