If this is the 83-key XT or the 84-key AT, then the spacebar has a complicated "undercarriage" assembly attached from the opposite side of the plate. Yes, you will have to take the keyboard apart to fix it.
I have not had an AT apart in quite a while, so please correct me if I am wrong, but I am pretty sure that it has the same tabs. There is probably a plastic hold-down tab on each side that has a slot for the wire to slide in. If your problem is on one side, that tab may be loose, broken, or lost.
It has a slightly flared oval base that force-fits through the plate. If it is broken or missing, you will need to fabricate a replacement, I have bent a small slice of sheet metal into a "Z" shape and epoxied it to the plate. That is what I am typing on now, and it works well on my F-122.
edit - Oops, I was wrong. No hold-down tabs. But the tab replacement still works well with other models.