The Chiefs' $782,809 in cap space is not very much at all. Compare it to the Jaguars or 49ers who both still have a whopping $52 million in cap space, according to NFLPA records. The Chiefs are in the better position than those two teams. The Chiefs know they are a good team and believe they have a shot to make a run.
It doesn't do you much good to have a ton of cap space right now because there is no one to spend it on. The first big wave of free agency is over. The cost of your draft picks is already set.
So what else do the Chiefs need money for?
Draft picks. Only the top 51 players count against the cap right now so once a draft pick is signed he will bump someone out of the top 51. Thus, the Chiefs don't need as much for draft picks as you would think. It's around $2 million.
Free agents. There will be a veteran free agent or two signed. The Chiefs are at 79 players and they are allowed to have 90 in the offseason. They will fill that roster out.
Injuries. The Chiefs are going to go into the season with some cap space to prepare for a player getting injured and needing to sign another player. They'll be prepared for that.
So where can the Chiefs get more cap space? The easy answer here is a new deal with Eric Berry. Given this cap space situation, it seems more likely that something gets done with Berry simply because they need to lower his $10.8 million cap number.