I know it's a bit hard to try to predict what Ainge is thinking, but we can guess at what are the limits on the kind of deals he would do by the trading deadline.
1) Salary cap rules. This is the most obvious constraint on Ainge's deal making.
2) Refusal to take on a bad contract beyond this season. Ainge values cap flexability for this off-season. This refusal to take back salary is one reason why I'm not sure if any expiring contracts are worth a first round pick. Last season, Houston got a first round pick from Memphis in a rental of Shane Battier, but they had to take on the $5m that is owed to Hashem Thabeet for this season. Unlike some people, I see Thabeet more as trade ballast than a good asset. Some people like the idea of trading Ray Allen to Chicago for Kyle Korver and Ronnie Brewer (whose contracts combined are guaranteed only $500K for next season), and a first round pick. I tend to believe that the market price for a rental of Ray Allen is only a second round pick, unless the Celtics are willing to take back Rip Hamilton's guaranteed $5m for next season (and $1m for the season after that).
3) Refusal to deal a first round draft pick. I tend to think that Ainge doesn't want to part with draft picks, even late draft picks, which I think are severely underrated by some, since there's probably a 50-50 chance that you get a player who can be at least an acceptable rotation player for a peak of 2-3 seasons with one of the last ten picks in the first round. You are unlikely to get a star, but you probably have at least a 1-in-3 shot of getting someone at least as useful as Delonte West or Nenad Krstic.
4) Intention to acquire young players that he doesn't plan on keeping. The Celtics don't have the sort of assets to acquire a player who will be a foundational building block, so the team needs to be focused on "winning" some small trades and steadily building up value. When it was reported that Ainge offered Ray Allen to Indiana for Tyler Hansbrough and a first, several posters noted that Hansbrough isn't the kind of young guy you want to build around. Well, no, but I imagine that Ainge envisions putting together a package of Hansbrough, JuJuan Johnson, and multiple draft picks and turning that into a player already under contract instead of Hansbrough being a Celtic for several years.