Stern said last month the league wants player costs to drop $750-800 million.
"We definitely don't agree with those numbers," Evans said. "We feel like the game is really at a great place."
Evans, a vice president on the NBA Players Association executive committee, said the two sides may not be able to make any substantial progress in the NBA labor talks until the February All-Star break, when all players are available to return to the negotiations.
He said the league's relationship with fans would be damaged by a lockout, especially in the tough economy.
"If we have a lockout, it's just going to set us back," Evans said while distributing 1,000 Thanksgiving turkeys to Atlanta-area families in a program sponsored by the NBPA and the Boys & Girls Clubs of America. "With the state the economy is in, fans are not going to want to keep getting slapped in the face with players and NBA teams, as fortunate as we are financially to even be playing a game for a living, to keep throwing it in people's face that we're not making enough money, whether it be the league or whether it be the players."
Evans, a seven-year veteran currently recovering from offseason knee surgery, said he has attended all the negotiating sessions open to players.
He called Stern's tough talk "just a negotiation tactic."
"The tone just depends on the perspective, our tone or their tone," Evans said. "Obviously in Stern's words right now we are far apart, but who's to say we'll still be far apart in June or July of ?"
Evans predicted there will be progress in February "because that's a time period in which a lot of heavy hitters per se will be able to come in."
"Everybody will be able to be there and hopefully we'll be able to make some headway," he said.
League owners are seeking major changes to the current CBA that expires June 30. Deputy commissioner Adam Silver said the league has told the union that owners project league-wide losses of about $340-350 million this season.
Billy Hunter, the executive director of the players association, has said the league's stance could lead to a work stoppage.
Evans wouldn't rate the odds of a lockout.
"We don't want to encourage a lockout at all," he said.
Evans said some teams' finances have been hurt by bad decisions.
"What we do believe is with the current system in place there's enough restraints within the system that they can police themselves," Evans said. "The system has proven to work that we have in place. Hypothetically, if a GM has approved a bad contract, yes it's going to reflect poorly on your franchise."
Evans and Hawks teammate Etan Thomas both distributed turkeys Tuesday as part a campaign sponsored by the NBPA. During the campaign, players will distribute turkeys to more than 8,000 families in NBA cities.