Per sportrac the Bears
were $3.6M under the salary cap in 2015. It's important to know that cap room does move to the next year so it can be used, but I'm pretty sure at the end of the 2016 season the Bears will have additional cap room again.
What does that extra cap space get you? Did that $3.6M in space help get a win on the field? No. It's not an exact measure, but was that money that the ownership essentially didn't have to accuont for as an expense? Yes. With the revenue number being what it is does that mean the ownership will keep a bit more? Yes. Will you as a fan see that money either as a better product on the field or in ticket prices being lowered? No.
IMO if teams were to spend to the cap then it's more of a fight for limited resources. Teams are choosing to not pay these players because they would rather have cap space, which ultimately the fans never get the benefit of.
Last year there were 3 teams with $20M+ in cap space available (Jax. Cle, and Tenn). They all sucked. Meanwhile the 2 teams closest to the limit, Arizona and Seattle, just happened to be two of the better teams in the league.
If you have a talented player on your team that can help you win you should pay them. Granted players will always ask for more, but as Windy pointed out that's the negotiation process. If a player is a FA and is getting offered more from another team then why should they stay? Clearly the other team wants them more, so they are entitiled to get paid more in a place they are appreciated more.
As a fan if you feel that player can make your team better why do you care how much he's being paid? Seriously. If the team is winning who cares what he's being paid. If they are losing then they can easily cut him for underperforming. These contract have little long term guarantee, so you can easily make that move when needed, but whenever a player threatens to hold out fans act like the player just cheated on them.
Let's use my Eagles as an example. Jeremy Maclin left the team because he was ~$1M/season 'too expensive'. Eagles finished the season with $9.5M under the cap (and $18.9 in dead cap space). Maclin's cap number for 2015 was $3.4M. Last year we lead the league in drops with 66, didn't have a real impact WR, lost twice to Washington in a very winable NFCE race and are going through a complete overhaul.
Maclin was ~$1M/season too much... Okay.... As a fan I'd rather they have paid the money and not put me through such a shitty season.
Let's take my Maclin example and look to apply it to Miller or maybe a closer comparison, Jeffery. What's $1M/season if that player gives you a better chance of getting a win on Sunday? Would you rather have 'cap space' for future contract than talent on the field? I get you want to align cap space with future expenses like a franchise QBs contract or another big contract coming due, but that ~1M/season impacts the quality of the product this season, not in future years where it might make a difference.