I take it that you mean the parking garage. Whether or not its full seems to be more seasonal...i.e. the only times I've seen it full have been on holidays. The outer lots always fill up first; once, they even let us park in the garage at the outside lot rate because all the other lots were full and there was plenty of space in the garage.
As an alternate, consider Midway ParkSavers, which is right across the street from the garage and the Orange Line train entrance. Once we learned about that lot, we stopped parking at the Midway-owned ones. You can find a coupon for a free day of parking there on ATA's website.
Barb