Barbara,
I like your idea. It may work for me. Let me see if I have this correct...

1. Patient calls your office. Your office's answering machine states that it's closed, call 911 if it's an emergency, and then instructs the patient to press a number if they want the call fowarded to the on-call person.
2. Phone gets fowarded to your cell phone where it could be answered in a timely manner (you pick up or answer the message--and I presume you leave a message on the cell phone stating that they could leave a message if the patient will leave their phone number AND they deactivate their call block.
3. If you are not on call, then the office answering machine forwards it to the on-call physician or the on-call physician's answering machine.

By doing this you get rid of the pager and answering service.
I like it!