It's just posturing to put more pressure on the players. There's no way they'd institute a hard cap so low that teams would have to give up core players. Even if the cap were that low, they would not force teams to cut players to get under the cap. There'd likely be a period during which teams could be over the cap, but they wouldn't be allowed to re-sign players and stay over the cap.
The most extreme thing they'd do is make the latter years of the superstar's contracts non-guaranteed so a team would be able to waive them to get under the cap. In any case, nothing would happen right away.
As you said, Stern has no interest in breaking up superteams.
In the long run, however, I'm sure he'd like to see a league more like the NFL, where almost every team has one really good player and they try to build around him with mediocre to above average players.
That way everybody has a solid chance at winning each year, and winning is more about the way your role players complement your superstar and less about having more overall talent than the other team.