Welcome to the forums. You're talking to other customers here.
Verizon, like most large ISPs and cable companies, offers new customer discounts that expire after a year or two. The offered discounts and terms vary due to market conditions. The do not offer these discounts to existing customers. The discounts may or may not be linked to a two-year contract. If you are under contract, there may not be much you can do.
However, they do sometimes offer discounts to existing customers to keep them from leaving. If you are out of contract or within a month or two contract expiration you may be able to get one of these "valued customer discounts." The best way to do this is to investigate what the competition is offering new customers and then call Verizon's customer retention department. This is the department that handles cancellations and works to keep customers from leaving. They often have more options than the standard reps. It helps if you really are prepared to switch to another company when you call.
Oh, and I wouldn't worry Verizon's representatives pay check. That's between Verizon and their employees, not you. You need to do what's best for your wallet, not theirs.
Verizon will not drop the early termination fee (ETF).
Since you're under contract, that explains why they aren't offering anything. See if you can find documentation of the promotions that were active when you signed up. If you have something that says they were for 24 months, you should be able to get Verizon to honor that. If the promotions were for 12 months, then you're stuck with the plan you have unless you pay the ETF.
Remember to be polite when you talk to Verizon. Raised voices and arguing will get you nowhere fast.
Even if you're out of contract they're not willing to do anything for you.
It depends on when you call and maybe even who you talk to. They have different "valued customers discounts" at different times of the year. Sometimes they offer free HBO, sometimes not. I recently negotiated a discount and free HBO along with a speed bump to 75/75, so I know it's quite possible.
I get "valued customer discounts" by calling retention. Sometimes it takes several calls over several months, but they do give discounts. One time when I called and the discount offered wasn't great, the rep suggested I call back in a month. I did that and got a larger discount.
My suggestion is to call retentions every few weeks or so until you get their best offer. Always be polite and courteous as you want the rep on your side. If you have an "attitude" or get angry, they will be very unlikely to want to do anything for you. Remember, they are people too.
If you agree to anything, be sure to get it in an email. Make sure you understand the duration of any discounts of free premium channels. That will avoid surprises later.
Finally, know what the competition is offering. If it's better, you can and should use that as leverage. You should also be prepared to switch. VZ most likely won't counter, but you'll get a better deal one way or another!