As Bryan Preston reports, it does so because:
the Obama campaign’s web site lacks the security code field. The [Republican candidates] require it, and will not accept donations unless the security code and payment information match up.
Obama’s campaign implemented the same lack of verification in 2008, but the mainstream media never called them on it. It appears as though that episode has prompted a repeat in 2012.
It also means that Obama donors can easily circumvent federal limits placed on the amount one can donate to a candidate by simply using different names.This means three things are likely true. One, the Obama campaign disabled the verification system. The verification system is turned on on web sites that accept credit cards, by default. I used to manage the website for the Texas Republican Party, so I know this from personal experience. Someone had to take the action of turning it off on the Obama site. Two, the Obama campaign can accept donations without the identity of the donor being positively verified. Three, not only can people in foreign countries donate to the Obama campaign in violation of federal campaign law, so apparently can identity thieves who have access to stolen credit card numbers. People who do not know that their credit cards have been compromised may not notice small amounts in the $3 dollar donation range that the Obama campaign has been targeting, when such donations show up on their statements.