I have Verizon and have used its Global Plan since 2009 for our trips to Europe. I was never offered a calling card and like others have said, I can't imagine why you would need one. Depending on where you stay, your hotel or host may even have free calls to the US using their landline. In some cases it is bundled in with other communication and entertainment electronic services at no extra charge for them.
What most have said about the clueless general service people is absolutely correct. There are many options on the Global Plan and the couple of times I had them do it, they failed to get all the pieces together. The Global Plan people know what they are doing and when I used them everything turned out okay. Everything also turned out okay when I set it up online myself.
On all those trips in the past I used a years old global-ready flip phone. This next one will be using a global- ready Moto X. I got the smart phone (much to my husband's dismay) because the past couple of years the hotels or hosts where we were staying requested a text message in advance of our stay there. They consistently preferred that over a phone call or an email.
Another thing, your lodgings may have free Wi-Fi in your room or somewhere else in in the building. Just like here, it may be iffy in some locations. You don't really have to go to a more public place if it works okay unless you just want to do that. Oddly, it has been our experience that more expensive hotels tend to both have a charge for the in-room Wi-Fi and have the worst Wi-Fi service.
Here's the link to the Global Services info at Verizon for anyone who might need it: http://www.verizonwireless.com/wcms/global.html. It is not very easy to find if you go into their website from the beginning.