The hacker group Syrian Electronic Army has announced, through their Twitter account, that they have compromised the email of barackobama.com. They appear only to have compromised the account of one member of the organization.
The domain barackobama.com was the President's election and re-election campaign site. Since then it has been turned into an advocacy organization, Organizing for Action, to promote the President's agenda.
The image accompanying the tweet is a screen grab of a Gmail account email@example.com. This indicates what was known before, that the domain is managed by Google Apps. One of the messages specifically refers to a Suzanne Snurpus. Ms Snurpus appears to be involved in Organizing for Action and hosts events at her house in North Augusta, SC.
She doesn't appear to be a big deal in the organization, nor does it seem she has anything to do with the government. There's no reason to believe that anything other than this one email account was compromised.
UPDATE: The AP is reporting that the SEA is also responsible for modifying the links in tweets from @barackobama. We just examined the feed and all the links appear correct, so perhaps the problem has already been solved.