Construction costs are not going to be significantly lower at all on a project like this than any time in the recent past. At first glance, someone would say of course, construction is slow, so obviously the contractors will drop their prices because they all need the work. This is true to an extent, but not enough to make any discernible difference to the public.
As this project will be at least partially public funded, all the labor will be subject to prevailing wage rates, which is a predetermined wage rate negotiated for the most part between labor unions and the state. These rates include a certain amount of raise every year, which once again is predetermined, and will take effect no matter how good or bad the construction industry is doing at the time.
Material prices really aren't much lower, for the most part, than they have been in the past. In fact, metal prices are once again on the rise, which affects everything from copper wire to rebar to ductwork to the structural steel in building, and concrete is also on the rise again. Add to that the rising fuel costs and I would expect the material costs for this building to be as high as they have ever been, possibly barring acouple years at the peak of the boom. These suppliers have had plenty of time to adjust, and have just backed off their production in order to keep the prices as high or near as high as they have ever been.
So with not much chance of saving money in either labor or material costs, the only real way to save at all is by the contractor/subcontractors willing to lower their profit margins in order to get the job. The problem here is that this project will be huge, and there are only a limited number of companies in each phase of the construction that are able to do a job this big. Sort of an oligarchy if you will, and of these few companies able to do the work, these were exactly the business model that was hit the hardest by the construction slowdown, and where there were maybe 4 masonry contractors 6 years ago in Northern California that could handle a job like this, now there are probably only 2, and both of these guys need all the profit they can get, so you're not really going to see much savings here either. (This was just hypothetical, I'm not sure how much masonry will even be in the building, but its the same for most trades)
Bottom line here is that prices are always rising, and just because there are a bunch of out of work house framers around doesn't necessarily mean that anything will cost less.