Verizon uses CDMA and LTE technology and does not use GSM/UMTS technology so therefore VZW does not sell SIM cards or phones not sold by them on their network.
The only GSM networks in the US are AT&T and T-Mobile and they have prepaid offers. Please note that most prepaid offers like T-Mobile or AT&T in the US are limited by data volume. Or you can use a 3rd party MVNO riding on AT&T or T-Mobile's networks.
Please also make sure that your phone must has the North America 850 / 1900 bands for 2G GSM/EDGE, 3G UMTS/HSPA+ and 4G LTE (AWS or Verizon and AT&T's proprietary band). These are different than the Europe/Asia/Rest of the World 900/2100 Bands. If you want better signal / more capacity on T-Mobile you need to have a phone with a North America specific 1700/2100MHz AWS band (not likely to be on phones not sold in North America unless you have a Google Nexus, or a Nokia Pentaband phone etc.).