Yep your SLA should have you reaching for the phones every fracking second, as I too used to work (and still do kinda) in call centres and technical support. With a possible 30 minute troubleshooting call, it is important to have that many needy customers.
No calls means eventually no job, unless you are also working in the QA or on-site support, which could be a mixed blessing.

One of my tech jobs was like that, as I was the only one taking calls for the entire USA and Europe (3am-4pm) and only when the KPI's started going south, did I get any help. After a while the calls stopped (my excellent skills at work) and I laid off the entire crew. I threw a party for all their hard work and gave them their pay and bonus and said cya.
One of life's picture perfect moments.
I could be wrong, but like Chad implies - with what you are remarking, you will be outsourced. Don't feel too bad if it happens, but make sure you have some cash saved. A colleague of mine had the same thing done to him (not by me) and he lost everything and is currently pushing a supermarket trolly up the strip.
