I remember visiting a site a while back that offered to do phone support for web host company and would do it it there own brand. I.e. Someone phoned up and 800 number and was put through to the call centre, call centre would note it was a nothrillshost number and would answer the phone "Thanks for calling No Thrills Host Support, How can we help" etc.
There are only few Support Companies capable of handling 24x7 phone support of web hosting companies and you will need to find out those companies from this forum. Visit them on live chat or give them call and ask them if they will provide dedicated phone support to your customers and how will they respond to phone calls if you wish to setup dedicated line with them.