NEW YORK - A whole new round of back-and-forth began: a final offer, a rejection. A counterproposal, a rejection. With just hours before the NHL was set to cancel the season, the league and the players' association were still far apart.

But they were talking.

Early Tuesday evening, the league had made a take-it-or-leave-it pitch of a $42.5 million salary cap to the players' association. The union responded with a cap figure of its own: $49 million.

The league dismissed that out of hand, saying all teams couldn't afford that much.

"If every team spent to the $49 million ... total player compensation would exceed what we spent last season," NHL commissioner Gary Bettman said in his second letter of the day to NHLPA executive director Bob Goodenow. "We cannot afford your proposal."

Goodenow disputed Bettman's claim in a letter, taking a hard-line stance and replying, "You will receive nothing further from us."

"Clubs are spending significantly less than your team payroll limit number of $42.5 million," Goodenow said in his second letter. "I am at a loss to understand how you suggest your offer earlier today represents a $75 million dollar increase when it only impacts the spending of nine teams!"

The exchange began with the first real positive news of the lockout early Tuesday, when the players' association accepted, for the first time, the concept of a salary cap. That concession came after the NHL dropped its demand that league revenues be linked to player costs.

So the players offered a $52 million dollar cap; the league countered with its final offer of $42.5 million.

"We wish that the NHL had offered a 'no linkage' proposal before yesterday so that negotiations in that arena could have commenced sooner," Goodenow said in his first letter to Bettman. "However, we recognize that they did not and we agree that time is short."

The league had bumped its salary-cap offer up from $40 million and gave the union until 11 a.m. today to accept. Bettman said if the offer was rejected, the season would be canceled two hours later, according to a letter he sent to Goodenow.

In his first letter, Bettman said there was no time or flexibility for bargaining.

"This offer is not an invitation to begin negotiations - it's too late for that," Bettman said. "This is our last effort to make a deal that's fair to the players and one that the clubs (hopefully) can afford. We have no more flexibility and there is no time for further negotiation."

In the union's counteroffer, teams would still be allowed to spend up to 10 percent above the threshold, but they would only be able to do it twice during the six years of the deal and would be subject to an escalating luxury tax on anything above $40 million.

The players' original soft-cap proposal on Monday permitted teams to go over the threshold three times.

The union's offer would also require the 30 teams to have a minimum payroll of $25 million, but clubs would be allowed to drop no more than 10 percent below the total twice during the deal.

Bettman scheduled a news conference to with the intention of announcing that there wouldn't be any hockey until at least next fall.

"Hopefully, the press conference will not be necessary," Bettman said in his letter.

That shifted the pressure to the players, some of whom stated Tuesday they were surprised that the union accepted a salary cap this late in the game.

"We probably could've gotten this thing done in the summertime," Chicago forward Matthew Barnaby said. "I'm just a little disappointed that it went this far to play poker and to have someone call your bluff."

Now the sides are faced with a hard deadline to make a deal and salvage a season that was already going to be cut from 82 games per team to 28.

A central component to all offers is a 24 percent rollback on existing contracts that was first presented by the players' association in its Dec. 9 framework. On the adjusted scale, only eight of the 30 teams would have finished last season above $40 million. The average team payroll was $33.95 million, with the rollback factored in.

Without the rollback, the Detroit Red Wings had the highest payroll at the end of last season with $82.9 million; Pittsburgh was the lowest at $21.65 million.

If a deal is not reached, the NHL would become the first major professional league in North America to lose an entire season because of a labor dispute. The Stanley Cup has been awarded every year since 1919, when a flu epidemic canceled the finals.

As of Tuesday, the 153rd day of the lockout, 834 of the 1,230 regular-season games and the All-Star game already have been lost to a lockout that started Sept. 16.