The thing with cell phones you purchase at Target, Wal•Mart, Best Buy, etc., is they're unlocked only in the sense they haven't been connected to a carrier yet. Once a carrier has been set up, the phone becomes locked to that carrier.
This unlike an unlocked phone you purchase directly from Apple, which will always be unlocked.
I found a discussion elsewhere about a person who could not get their phone unlocked by CC. They received this email:
From the Consumer Cellular Terms
"If you bought a Device from us, it may have been programmed with a SIM lock that will
prevent it from operating with other compatible wireless telephone carriers’ services.
If you wish to use this Device with the service of another wireless telephone carrier, you
must enter an unlock code. We will provide the unlock code upon request, provided that you meet certain criteria including, but not limited to the following:
(a) you have paid for your Device in full;
(b) the equipment has been active on Consumer Cellular’s service for at least six
months and the account is in good standing (i.e., it has no past due amount or unpaid
balance owed to Consumer Cellular);
(c) your Device has not been reported lost or stolen; and
(d) Consumer Cellular has the unlock code or can reasonably obtain it from the
manufacturer.
We may allow you to pay a fee in lieu of the above criteria. The fee will be set by us
in our sole discretion. For further details on eligibility requirements and for assistance
on obtaining the unlock code for your Device, please call 1 (800) 686-4460."
You can at least use this as a starting point to possibly figure out why they can't, or won't unlock it.