If I threaten to close my bank account, do you think the bank will cancel its proposed fee increase?

Like any other industry, that would depend on the individual bank, and individual banker, you deal with. I run a small community bank in NY, we value our customers and will try to find common ground as often as is possible. Most banks have begun imposing new fees to make up for lost fee income they used to receive when a customer overdrew their account with a debit card. This type of fee income is now illegal, and so you are seeing new fees. I would guess they can not, or will not negotiate with you, so close your account, and go to a small local bank where you will be well treated. In fact if you go to the new bank first, they just might be able to help you switch banks more seamlessly and with less frustration, I would if you came to me.