Quite recently, Twitter revealed that it too was the victim of an attack and that data on 250,000 accounts was leaked. Twitter asked all those users to reset their passwords, but it seems that the attack hit a little too close to home for Twitter.Apparently, it is now thinking of implementing a two-step or two-factor authentication system, like Google, Facebook, Yahoo, Dropbox and others already offer.
With this system, an attacker would need more than just the password to compromise an account, a secondary code is needed. Users get this code via their phones normally, either through an SMS, a dedicated app like Google Authenticator, or the regular mobile app, like Facebook does.
Twitter has a job ad for a software engineer focusing on security. In the ad, it lists a multifactor authentication scheme as one of the things the future employee would be working on.
This indicates that it's going to take a while for the feature to be rolled out, perhaps a few months, but it's safe to say it's coming.