At&t and Verizon on one dual SIM phone

I travel quite a bit around the US and find myself ending up in fairly rural places with limited service. I have been looking for a solution that will allow me to have one phone with two SIMs. One SIM ideally would be part of Verizon's CDMA network and he other At&t's GSM network. Can anybody point me in the right direction on how I can get this rolling or at least let me know if this is even possible?

Thanks a lot.