A CVV wouldn't make a difference for that, and given that US citizens live all over the world, there's realistically no way to prevent illegal foreign donations.
What would you use? Name? American have all sorts of names. Credit card billing address? Americans live abroad. IP? Americans live abroad. SSN? Fakeable (ask a restaurant dishwasher in NYC), and I dunno if you can ask for it.
http://www.breitbart.com/Big-Government/2012/10/08/Report-Il...
The GAI report recommends election officials: -Integrate safeguards to limit the solicitation of money from foreigners by requiring donors with foreign IP addresses to provide proof of U.S. citizenship before they can proceed to the donate page
-Immediately require campaigns to use industry-standard anti-fraud security technologies including, but not limited to, the Card Verification Value (CVV) and a rigorous Address Verification System (AVS)
-Immediately require all campaigns to retain and disclose identifying information on all online campaign contributions, including those falling under the $200 nondisclosure threshold currently allowed under federal law
-Address the threat of "Robo-Donations": The absence of industry-standard anti-fraud credit card security features render campaigns more vulnerable to so-called “robo-donations.” Robo-donations are large numbers of small, automated donations made through the Internet to evade FEC reporting requirements.
> Though not required by law, OFA requires a copy of a valid passport from any contributor who has been affirmed as eligible but donates with a mailing address outside the U.S. If they do not offer in one in a timely manner, the donation is returned.
The big question, as with voter fraud, is really "is this happening much at all?" I suspect the answer is similar to that of voter fraud - "nope".