Hacker group DERP has taken responsibility for the attacks via their, claiming to have "directed the Gaben Laser Beam at the EA login servers".
EA Support is working to resolve the issue according to their own twitter feed.
@AskEASupport Thank you for acknowledging the issue, even the EA Help Center wont load to shed any light. Keep the community informed pls.— Stefan Poziomka (@Stef_pozi) January 3, 2014
DERP have used similiar DDOS attacks to bring down games and services in the past. This time the motive appears to be support for Origin's rival distribution service Steam, according to further tweets on their twitter feed.