No, its not possible.
Currently, in the US, Verizon is a CDMA network. All of their towers are CDMA , there is no Verizon GSM so the iPhone would not work on the Verizon network. The SIM cards you are probably seeing are for the phones which have GSM and CDMA radios (I believe Verizon offers a Blackberry like this). That way you can use your phone internationally on a foreign GSM network.
Edit:
Verizon state they have plans to roll out GSM once they upgrade to a 4G network