There's a simple rule of thumb for determining when the Illinois Supreme Court will rule on a given case, and it's that there is no rule of thumb for determining when the Illinois Supreme Court will rule on a given case.
Most opinions come within a matter of months, but every now and then one takes much longer. The court heard oral arguments in the billion-dollar class action Avery v. State Farm in May 2003; a decision didn't come until August 2005. Last year, the excellent Appellate Strategist blog, written by attorney Kirk Jenkins of Sedgwick LLP, calculated the average time-to-decision in 2013:
As always, the court produced decisions much more quickly in 2013 when there was no dissent. Unanimous decisions came down an average of 103.7 days after oral argument, while cases with dissenters took much longer — 185.8 days after argument. The court’s average lag time on nonunanimous decisions has been relatively static since 2011, but the average lag time on unanimous decisions has been cut by more than three weeks in that time.
I'd guess that with the high profile of the pension case, and the court already having granted an expedited hearing schedule, that barring some unusual outcome, an opinion will come in fairly short order. In fact, it wouldn't surprise me if a draft opinion was already being written before Wednesday's arguments, based on the briefs.
The Illinois Supreme Court does not assign opinion writing like at the U.S. Supreme Court, where the chief justice decides who gets the job (assuming he's in the majority, otherwise the longest-serving justice in the majority makes the pick). Rather, the justices catch cases in a regular rotation. That usually means by the time of oral arguments, a justice will know if he or she is expected to write the opinion (again, assuming that opinion will attract the constitutionally required four justices needed to issue a ruling).
According to my notes, Justice Bob Thomas asked the greatest number of questions during Wednesday's pension arguments, followed by Chief Justice Rita Garman and Justice Lloyd Karmeier. This is pure speculation, but it would not surprise me to see Thomas writing the main opinion, or perhaps Garman or Karmeier. But again, that's just speculation.
The fact is, as with so many things involving the Illinois Supreme Court, there are a very small number of people who know what'll happen before the court makes an official announcement: the justices, their individual clerks, and a handful of court staffers, including the court clerk and the reporter of decisions. Until the justices are ready to make their opinion(s) public, the rest of us will just have to wait.